Functional analysis and transforms Books
Princeton University Press Spaces of PL Manifolds and Categories of Simple
Book SynopsisSince its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing WaldhauTrade Review"The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology."--Michael Weiss, Jahresber "It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program."--Bruce Hughes, Zentralblatt MATHTable of ContentsIntroduction 1 1.The stable parametrized h-cobordism theorem 7 1.1. The manifold part 7 1.2. The non-manifold part 13 1.3. Algebraic K-theory of spaces 15 1.4. Relation to other literature 20 2.On simple maps 29 2.1. Simple maps of simplicial sets 29 2.2. Normal subdivision of simplicial sets 34 2.3. Geometric realization and subdivision 42 2.4. The reduced mapping cylinder 56 2.5. Making simplicial sets non-singular 68 2.6. The approximate lifting property 74 2.7. Subdivision of simplicial sets over DELTAq 83 3.The non-manifold part 99 3.1. Categories of simple maps 99 3.2. Filling horns 108 3.3. Some homotopy fiber sequences 119 3.4. Polyhedral realization 126 3.5. Turning Serre fibrations into bundles 131 3.6. Quillen's Theorems A and B 134 4.The manifold part 139 4.1. Spaces of PL manifolds 139 4.2. Spaces of thickenings 150 4.3. Straightening the thickenings 155 Bibliography 175 Symbols 179 Index 181
£68.00
Princeton University Press Advances in Analysis
Book SynopsisPrinceton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. This volume gathers papers from internationally renowned mathematicians, many of whom have been Stein's students.Table of ContentsPreface ix Chapter 1 Selected Theorems by Eli Stein 1 Charles Fefferman Chapter 2 Eli's Impact: A Case Study 35 Charles Fefferman Chapter 3 On Oscillatory Integral Operators in Higher Dimensions 47 Jean Bourgain Chapter 4 Holder Regularity for Generalized Master Equations with Rough Kernels 63 Luis Caffarelli and Luis Silvestre Chapter 5 Extremizers of a Radon Transform Inequality 84 Michael Christ Chapter 6 Should We Solve Plateau's Problem Again? 108 Guy David Chapter 7 Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms 146 Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger Chapter 8 Internal DLA for Cylinders 189 David Jerison, Lionel Levine, and Scott Sheffield Chapter 9 The Energy Critical Wave Equation in 3D 215 Carlos Kenig Chapter 10 On the Bounded L2 Curvature Conjecture 224 Sergiu Klainerman Chapter 11 On Div-Curl for Higher Order 245 Loredana Lanzani and Andrew S. Raich Chapter 12 Square Functions and Maximal Operators Associated with Radial Fourier Multipliers 273 Sanghyuk Lee, Keith M. Rogers, and Andreas Seeger Chapter 13 Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in 3, and Newton Polyhedra 303 Detlef Muller Chapter 14 Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length 346 Camil Muscalu, Terence Tao, and Christoph Thiele Chapter 15 Diagonal Estimates for Bergman Kernels in Monomial-Type Domains 402 Alexander Nagel and Malabika Pramanik Chapter 16 On the Singularities of the Pluricomplex Green's Function 419 D. H. Phong and Jacob Sturm Chapter 17 Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs 436 Fulvio Ricci Chapter 18 On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature 447 Christopher D. Sogge and Steve Zelditch List of Contributors 463 Index 465
£90.00
Princeton University Press Riemann Surfaces
Book SynopsisThe theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special characTable of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Surface Topology, pg. 1*Chapter II. Riemann Surfaces, pg. 112*Chapter III. Harmonic Functions on Riemann Surfaces, pg. 148*Chapter IV. Classification Theory, pg. 196*Chapter V. Differentials on Riemann Surfaces, pg. 265*Bibliography, pg. 332*Index, pg. 374
£55.25
Institute of Physics Publishing Principles and Applications of Fourier Optics IOP
Book SynopsisIn this text, Robert Tyson presents the fundamentals of Fourier optics with sufficient detail to educate the reader, typically an advanced student or working scientist or engineer, to the level of applying the knowledge to a specific set of design or analysis problems. Key results are presented with an explanation of the physical meaning and accompanied by appropriate literature references. The last half of the book explores some of the many and varied modern applications.
£89.10
John Wiley & Sons Inc Handbook of RealTime Fast Fourier Transforms
Book SynopsisTable of ContentsPreface. Overview. The Discrete Fourier Transform. The Fast Fourier Transform. Weighting Functions. Frequency Analysis. Linear Filtering and Pattern Matching. Multidimentional Processing. Building-Block Algorithms. Algorithm Construction. Arithmetic Building Blocks for Architectures. Multiprocessor Architectures. Algorithm and Data Mappings. Arithmetic Formats. Chips. Board Decisions and Selection. Test. Design Examples. Glossary. Appendix: Table of Comparison Matrices. Index.
£161.95
Springer Us Vector Bundles and Their Applications Mathematics
Book Synopsis1 Introduction to the Locally Trivial Bundles Theory.- 2 Homotopy Invariants of Vector Bundles.- 3 Geometric Constructions of Bundles.- 4 Calculation Methods in K-Theory.- 5 Elliptic Operators on Smooth Manifolds and K-Theory.- 6 Some Applications of Vector Bundle Theory.- References.Table of ContentsPreface. 1. Introduction to the Locally Trivial Bundles Theory. 2. Homotopy Invariants of Vector Bundles. 3. Geometric Constructions of Bundles. 4. Calculation Methods in K-Theory. 5. Elliptic Operators on Smooth Manifolds and K-Theory. 6. Some Applications of Vector Bundle Theory. Index. References.
£85.49
Springer Regularization of IllPosed Problems by Iteration Methods 499 Mathematics and Its Applications
Book Synopsis1 Regularizing Algorithms for Linear Ill-Posed Problems: Unified Approach.- 2 Iteration Steepest Descent Methods for Linear Operator Equations.- 3 Iteration Conjugate Direction Methods for Linear Operator Equations.- 4 Iteration Steepest Descent Methods for Nonlinear Operator Equations.- 5 Iteration Methods for Ill-Posed Constrained Minimization Problems.- 6 Descriptive Regularization Algorithms on the Basis of the Conjugate Gradient Projection Method.Trade Review`The book will be useful for specialists who in their theoretical and applied investigations deal with ill-posed and inverse problems.' Mathematical Reviews Clippings (2001)Table of ContentsPreface. Introduction. 1. Regularizing Algorithms for Linear Ill-Posed Problems: Unified Approach. 2. Iteration Steepest Descent Methods for Linear Operator Equations. 3. Iteration Conjugate Direction Methods For Linear Operator Equations. 4. Iteration Steepest Descent Methods for Nonlinear Operator Equations. 5. Iteration Methods for Ill-Posed Constrained Minimization Problems. 6. Descriptive Regularization Algorithms on the Basis of the Conjugate Gradient Projection Method. Bibliography. Index.
£42.74
Birkhäuser Basic Operator Theory
Book Synopsisrii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators;Table of ContentsIntroduction * I. Hilbert Spaces * II. Bounded Linear Operators on Hilbert Spaces * III. Spectral Theory of Compact Self Adjoint Operators * IV. Spectral Theory of Integral Operators * V. Oscillations of an Elastic String * VI. Operational Calculus with Applications * VII. Solving Linear Equations by Iterative Methods * VIII. Further Developments of the Spectral Theorem * IX. Banach Spaces * X. Linear Operators on a Banach Space * XI. Compact Operators on a Banach Space * XII. Non-Linear Operators * Appendix 1. Countable Sets and Separable Hilbert Spaces * Appendix 2. Lebesgue Integration and LP Spaces * Appendix 3. Proof of the Hahn-Banach Theorem * Appendix 4. Proof of the Closed Graph Theorem * Suggested Reading * References * Index
£68.88
Birkhauser Boston Inc An Introduction to the Uncertainty Principle
Book SynopsisIn particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant;Trade Review"This nicely written book by Thangavelu is concerned with extensions of Hardy's theorem to settings that arise from noncommutative harmonic analysis.... Each chapter contains several applications to the heat equation in various settings and ends with an extensive presentation of related topics, current research, detailed references to the literature, and lists of open problems. This makes the book an invaluable resource for graduate students and researchers in harmonic analysis and applied mathematics." —SIAM Review "…Each chapter ends with useful notes and open problems. Everything is written in sufficient detail to benefit specialized interested readers…" —MATHEMATICAL REVIEWS "The authoer discusses inthe present book the original theorem of Hardy and some of its generaliztions and its connections to noncommunitave analysis, harmonic analysis and special functions. First Hardy's theorem for the Euclidian Fourier transform is treated, and a theorem of Beurling and Hömander Subsequently Hardy's theorem is dicussed for the Fourier transfom on the Heisenberg group. finally the author discusses generaliztions of Hardy's theorem involving the Helgason Fourier transform for rank one symmetric spaces and for H-type groups. This unique book will be of great value for readers interested in this branch of analysis." ---Monatshefte für MathematikTable of Contents1 Euclidean Spaces.- 1.1 Fourier transform on L1(?n).- 1.2 Hermite functions and L2 theory.- 1.3 Spherical harmonics and symmetry properties.- 1.4 Hardy’s theorem on ?n.- 1.5 Beurling’s theorem and its consequences.- 1.6 Further results and open problems.- 2 Heisenberg Groups.- 2.1 Heisenberg group and its representations.- 2.2 Fourier transform on Hn.- 2.3 Special Hermite functions.- 2.4 Fourier transform of radial functions.- 2.5 Unitary group and spherical harmonics.- 2.6 Spherical harmonics and the Weyl transform.- 2.7 Weyl correspondence of polynomials.- 2.8 Heat kernel for the sublaplacian.- 2.9 Hardy’s theorem for the Heisenberg group.- 2.10 Further results and open problems.- 3 Symmetric Spaces of Rank 1.- 3.1 A Riemannian space associated to Hn.- 3.2 The algebra of radial functions on S.- 3.3 Spherical Fourier transform.- 3.4 Helgason Fourier transform.- 3.5 Hecke-Bochner formula for the Helgason Fourier transform.- 3.6 Jacobi transforms.- 3.7 Estimating the heat kernel.- 3.8 Hardy’s theorem for the Helgason Fourier transform.- 3.9 Further results and open problems.
£80.99
Birkhauser Boston Distributions Theory and Applications Cornerstones
Book SynopsisThe treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis.Trade ReviewFrom the reviews:“This is a fantastic book…Even in this enlightened age, the theory of distributions is a highly misunderstood and undervalued business…All of this notwithstanding, learning it from the extant standard sources has always been a rather an austere affair…Distributions: Theory and Applications is laden with examples and exercises…[The book] comes equipped with a long section containing solutions to selected exercises. Distributions: Theory and Applications is much more than a textbook for a one-semester introduction to the indicated subject: the reader/student who hangs in, reads the text while filling the margins and a notebook or two (or three, or four) along the way, and wrestles with the exercises, will be more than ready for more advanced works in the area as well as the business of applying distributions in a number of nontrivial settings. Additionally he will have been exposed to a great deal of serious mathematics from, if you’ll pardon the pun, all over the spectrum.”BLL — The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. —MAA Reviews“[Distributions: Theory and Applications] is a very useful, well-written, self contained, motivating book presenting the essentials of the theory of distributions of Schwartz, together with many applications to different areas of mathematics, like linear partial differential equations, Fourier analysis, quantum mechanics and signal analysis…One of the main features of this book is that many clarifying examples, presented with full detail, are included in the text. Moreover, a large number of problems is included at the end of each chapter…This reviewer found the book under review very stimulating, informative and inviting to further study. It is a very useful text for students who want to learn the theory of distributions, for experts in the abstract theory who want to read an application-oriented presentation with many examples and, last but not least, for mathematicians in related areas or theoretical physicists who need a self-contained, reasonable short presentation of the theory. I would strongly recommend it to all my colleagues.” —Zentralblatt MATH “The aim of this book is to present the theory of distributions of Laurent Schwartz in a rigorous, accessible way, together with applications to linear partial differential equations, Fourier analysis, quantum mechanics and signal analysis. The text of Duistermaat and Kolk emphasizes applications to natural sciences like optics, quantum field theory, signal reconstruction or computer tomography. The exposition stresses applications and interactions with other parts of mathematics...It is a useful text for students who want to learn the theory of distributions, for experts in the abstract theory who want to read an application-oriented presentation with many examples, and also for mathematicians in related areas or theoretical physicists who need a self-contained presentation of the theory. The book includes many clarifying examples, presented in full detail. Many exercises and problems, with different levels of difficulty, are included at the end of each chapter. A reader who tries to solve them will re-examine many aspects of analysis of several variables in the light of the theory of distributions. Complete solutions of 146 of the 281 problems are provided and hints are given for many others.In summary, this is a useful, well-written, self-contained book about the theory of distributions of Schwartz and applications to different areas of mathematics and physics. Although there are many good books that present an introduction to the theory of distributions of Schwartz, assuming different levels of knowledge of linear functional analysis, the text of Duistermaat and Kolk is a very welcome addition. In the opinion of this reviewer, this is a stimulating, informative book that invites further study, and I strongly recommend it to any readers interested in this topic.” —Mathematical Reviews “This is a wonderful graduate level book providing a modern introduction to distribution theory with several entrance points for deeper tours into advanced analysis and applications. The lucid discussions of the development of certain key notions and the fine careful proofs define it as a valuable text book for a corresponding university course. … even in independent self-study the reader has a fair chance to obtain a reasonable amount of working knowledge … .” (G. Hörmann, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)“The authors have set out to produce a text on distribution theory accessible to undergraduate (or beginning graduate) students at the point in their studies where it could serve as an alternative to a beginning course in measure theory. … The authors discuss many fascinating results in distribution theory, with an emphasis on the use of the subject in linear PDEs … . The book succeeds both as a basic and as a rich account of results in distribution theory.” (Michael Taylor, SIAM Review, Vol. 54 (3), 2012)Table of ContentsPreface.- Standard Notation.- 1 Motivation .- Problems.- 2 Test Functions.- Problems.- 3 Distributions.- Problems.- 4 Differentiation of Distributions.- Problems.- 5 Convergence of Distributions.- Problems.- 6 Taylor Expansion in Several Variables.- Problems.- 7 Localization.- Problems.- 8 Distributions with Compact Support.- Problems.- 9 Multiplication by Functions.- Problems.- 10 Transposition: Pullback and Pushforward.- Problems.- 11 Convolution of Distributions.- Problems.- 12 Fundamental Solutions.- Problems.- 13 Fractional Integration and Differentiation .- 13.1 The Case of Dimension One.- 13.2 Wave Family.- 13.3 Appendix: Euler’s Gamma Function.- Problems.- 14 Fourier Transform.- Problems.- 15 Distribution Kernels.- Problems.- 16 Fourier Series.- Problems.- 17 Fundamental Solutions and Fourier Transform.- 17.1 Appendix: Fundamental Solution of .I?/k.- Problems.- 18 Supports and Fourier Transform.- Problems.- 19 Sobolev Spaces.- Problems.- 20 Appendix: Integration.- 21 Solutions to Selected Problems.- References.- Index of Notation.- Index.
£89.99
MP-AMM American Mathematical Studies in Duality on Noetherian Formal Schemes
Book SynopsisContains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. This book presents a self-contained treatment for formal schemes which synthesizes several duality-related topics, such as local duality, formal duality, residue theorems, and dualizing complexes.Table of ContentsPart 1: Duality and flat base change on formal schemes by L. Alonso, A. Jeremias, and J. Lipman Part 2: Greenlees-May duality on formal schemes by L. Alonso, A. Jeremias, and J. Lipman Part 3: Non-noetherian Grothendieck duality by J. Lipman Index.
£97.20
MP-AMM American Mathematical Spectral Theory of NonSelfAdjoint TwoPoint
Book SynopsisA monograph that develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. It lays the mathematical foundation in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators.Table of ContentsUnbounded linear operators Fredholm operators Introduction to the spectral theory of differential operators Principal part of a differential operator Projections and generalized eigenfunction expansions Spectral theory for general differential operators Bibliography Index.
£103.50
American Mathematical Society Orthogonal Polynomials and Random Matrices A
Book SynopsisExpands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models.Table of ContentsRiemann-Hilbert problems Jacobi operators Orthogonal polynomials Continued fractions Random matrix theory Equilibrium measures Asymptotics for orthogonal polynomials Universality Bibliography.
£32.36
MP-AMM American Mathematical Several Complex Variables with Connections to
Book SynopsisPresents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. This text includes a treatment of the local theory.Table of ContentsSelected problems in one complex variable Holomorphic functions of several variables Local rings and varieties The Nullstellensatz Dimension Homological algebra Sheaves and sheaf cohomology Coherent algebraic sheaves Coherent analytic sheaves Stein spaces Frechet sheaves--Cartan's theorems Projective varieties Algebraic vs. analytic--Serre's theorems Lie groups and their representations Algebraic groups The Borel-Weil-Bott theorem Bibliography Index.
£106.20
MP-AMM American Mathematical Zeros of Gaussian Analytic Functions and
Book SynopsisExamines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.
£54.90
Anthem Press A First Course in Functional Analysis Theory and
Book SynopsisThis book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.Table of ContentsIntroduction; I. Preliminaries; II. Normed Linear Spaces; III. Hilbert Space; IV. Linear Operators; V. Linear Functionals; VI. Space of Bounded Linear Functionals; VII. Closed Graph Theorem and Its Consequences; VIII. Compact Operators on Normed Linear Spaces; IX. Elements of Spectral Theory of Self-Adjoint Operators in Hilbert Spaces; X. Measure and Integration Lp Spaces; XI. Unbounded Linear Operators; XII. The Hahn-Banach Theorem and Optimization Problems; XIII. Variational Problems; XIV. The Wavelet Analysis; XV. Dynamical Systems; List of Symbols; Bibliography; Index
£63.00
Atlantic Financial Press Twenty Lectures About Gaussian Processes
£45.61
Cambridge University Press An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
Book SynopsisCovering the fundamental underlying theory as well as a range of applications, this unique text provides a unified overview of reproducing kernel Hilbert spaces. It offers an unrivalled and accessible introduction to the field, ideal for graduate students and researchers working in functional analysis or its applications.Trade Review'The purpose of this fine monograph is two-fold. On the one hand, the authors introduce a wide audience to the basic theory of reproducing kernel Hilbert spaces (RKHS), on the other hand they present applications of this theory in a variety of areas of mathematics … the authors have succeeded in arranging a very readable modern presentation of RKHS and in conveying the relevance of this beautiful theory by many examples and applications.' Dirk Werner, Zentralblatt MATH'Anyone looking for a nice introduction to this theory need look no further.' Jeff Ibbotson, MAA ReviewsTable of ContentsPart I. General Theory: 1. Introduction; 2. Fundamental results; 3. Interpolation and approximation; 4. Cholesky and Schur; 5. Operations on kernels; 6. Vector-valued spaces; Part II. Applications and Examples: 7. Power series on balls and pull-backs; 8. Statistics and machine learning; 9. Negative definite functions; 10. Positive definite functions on groups; 11. Applications of RKHS to integral operators; 12. Stochastic processes.
£60.99
The Mathematical Association of America The G. H. Hardy Reader
Book SynopsisG. H. Hardy ranks among the great mathematicians of the twentieth century, doing essential research in number theory and analysis. This book is a feast of Hardy's writing, featuring articles ranging from the serious to the humorous. The G. H. Hardy Reader is a worthy introduction to an extraordinary individual.Trade Review'The editors are to be congratulated on putting together this beautiful 'reader' with material from so many different sources, which illustrates so well the life, character and work of one of the great mathematicians of the twentieth century, Godfrey Harold Hardy (1877-1947). Even if you are familiar with Hardy's masterpiece A Mathematician's Apology or his book on Ramanujan, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work you will find a wealth of new and fascinating material in this 'reader' about Hardy.' Kenneth S. Williams, Canadian Mathematical Society NotesTable of ContentsPart I. Biography: 1. Hardy's life; 2. The letter from Ramanujan to Hardy, 16 January 1913; 3. A letter from Bertrand Russell to Lady Ottoline Morrell, 2 February 1913; 4. The Indian mathematician Ramanujan; 5. Epilogue from the man who knew infinity; 6. Posters of 'Hardy's years at Oxford'; 7. A glimpse of J. E. Littlewood; 8. A letter from Freeman Dyson to C. P. Snow, 22 May 1967, and two letters from Hardy to Dyson; 9. Miss Gertrude Hardy; Part II. Writings by and about G. H. Hardy: 10. Hardy on writing books; 11. Selections from Hardy's writings; 12. Selections from what others have said about Hardy; Part III. Mathematics: 13. An introduction to the theory of numbers; 14. Prime numbers; 15. The theory of numbers; 16. The Riemann zeta-function and lattice point problems; 17. Four Hardy gems; 18. What is geometry?; 19. The case against the mathematical tripos; 20. The mathematician on cricket; 21. Cricket for the rest of us; 22. A mathematical theorem about golf; 23. Mathematics in war-time; 24. Mathematics; 25. Asymptotic formulæ in combinatory analysis (excerpts) with S. Ramanujan; 26. A new solution of Waring's problem (excerpts), with J. E. Littlewood; 27. Some notes on certain theorems in higher trigonometry; 28. The Integral _∞0sin xx dx and further remarks on the integral _∞0sin xx dx; Part IV. Tributes: 29. Dr. Glaisher and the 'messenger of mathematics'; 30. David Hilbert; 31. Edmund Landau (with H. Heilbronn); 32. Gösta Mittag-Leffler; Part V. Book Reviews: 33. Osgood's calculus and Johnson's calculus; 34. Hadamard: the psychology of invention in the mathematical field; 35. Hulburt: differential and integral calculus; 36. Bôcher: an introduction to the study of integral equations.
£80.74
Cambridge University Press Introduction to Banach Spaces Analysis and
Book SynopsisThis two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.Trade ReviewReview of previous edition: 'Undoubtedly, the book will be very useful for all mathematicians (not only for postgraduate students) who work in the theory of Banach spaces, harmonic analysis and probability theory.' Anatolij M. Plichko, American Mathematical SocietyReview from previous edition: '… carefully written and edited … The exposition is clear, precise and lively, and the text makes very good reading.' Eve Oja, Zentralblatt MathTable of ContentsPreface; 1. Euclidean sections; 2. Separable Banach spaces without the approximation property; 3. Gaussian processes; 4. Reflexive subspaces of L1; 5. The method of selectors. Examples of its use; 6. The Pisier space of almost surely continuous functions. Applications; Appendix. News in the theory of infinite-dimensional Banach spaces in the past twenty years G. Godefroy; An update on some problems in high dimensional convex geometry and related probabilistic results O. Guédon; A few updates and pointers G. Pisier; On the mesh condition for Sidon sets L. Rodriguez-Piazza; Bibliography; Author index; Notation index; Subject index.
£83.59
Cambridge University Press Orders of Infinity The Infinitarcalcul Of Paul Du BoisReymond Cambridge Tracts in Mathematics
Book SynopsisOriginally published in 1910 as number twelve in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides an up-to-date version of Du Bois-Reymond's InfinitÃrcalcÃl by the celebrated English mathematician G. H. Hardy. This tract will be of value to anyone with an interest in the history of mathematics or the theory of functions.Table of Contents1. Introduction; 2. Scales of infinity in general; 3. Logarithmico-exponential scales; 4. Special problems connected with logarithmico-exponential scales; 5. Functions which do not conform to any logarithmico-exponential scale; 6. Differentiation and integration; 7. Some developments of Du Bois-Reymond's Infinitärcalcül; Appendix 1. General bibliography; Appendix 2. A sketch of some applications, with references; Appendix 3. Some numerical results.
£22.52
Cambridge University Press WignerType Theorems for Hilbert Grassmannians
Book SynopsisWigner''s theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.Table of ContentsIntroduction; 1. Two lattices; 2. Geometric transformations of Grassmannians; 3. Lattices of closed subspaces; 4. Wigner's theorem and its generalizations; 5. Compatibility relation; 6. Applications; References; Index.
£54.87
Springer Young Measures on Topological Spaces With Applications in Control Theory and Probability Theory Mathematics and Its Applications 571
Book SynopsisAims to provides applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).Trade ReviewFrom the reviews: "This book presents a wealth of results on Young measures on topological spaces in a very general framework. It is very likely that it will become the reference and starting point for any further developments in the field." (Georg K. Dolzmann, Mathematical Reviews, 2005k)Table of ContentsPreface. Generalities, Preliminary results. Young Measures, the four Stable Topologies: S, M, N, W. Convergence in Probability of Young Measures (with some applications to stable convergence). Compactness. Strong Tightness. Young Measures on Banach Spaces. Application. Applications in Control Theory. Semicontinuity of Integral Functionals using Young Measures. Stable Convergence in Limit Theorems of Probability Theory.
£42.74
Springer New York Fourier Analysis and Its Applications
Book SynopsisAt the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level.Trade ReviewFrom the reviews: "This book is one in the Graduate Texts in Mathematics series published by Springer. … There is a variety of worked examples as well as 350-plus exercises … . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts … without being totally opaque to the non-specialist. … The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006) "The author … presents the results of his experiences and choices for decades of teaching courses. … The tables and formulas collected … are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. … I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004) "This book is an interesting mixture of a traditional approach … and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. … The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004) "The book is appropriate for an advanced undergraduate or a master’s level one-term introductory course on Fourier series with applications to boundary value problems. … a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. … The book has a good collection of exercises … . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e)Table of ContentsIntroduction * Preparations * Laplace and Z Transforms * Fourier Series * L^2 Theory * Separation of Variables * Fourier Transforms * Distributions * Multi-Dimentional Fourier Analysis * Appendix A: The ubiquitous convolution * Appendix B: The Discrete Fourier Transform * Appendix C: Formulae * Appendix D: Answers to exercises * Appendix E: Literature
£49.49
Springer New York Concrete Functional Calculus Springer Monographs in Mathematics
Book SynopsisConcrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions.Trade ReviewFrom the reviews:“This monograph is a thorough and masterful work on non-linear analysis designed to be read and studied by graduate students and professional mathematical researchers. The overall perspective and choice of material is highly novel and original. … It is a unique account of some key areas of modern analysis which will surely turn out to be invaluable for many researchers in this and related areas.” (David Applebaum, The Mathematical Gazette, Vol. 98 (541), March, 2014)“The present monograph is quite extensive and interesting. It is divided into twelve chapters on different topics on Functional calculus and an appendix on non-atomic measure spaces. … The book has many historical comments and remarks which clarify the developments of the theory. It has also an extensive bibliography with 258 references. … will be very useful for all interested readers in Real-Functional Analysis and Probability.” (Francisco L. Hernandez, The European Mathematical Society, January, 2012)“The monograph under review aims at analyzing properties such as Hölder continuity, differentiability and analyticity of various types of nonlinear operators which arises in the study of differential and integral equations and in applications to problems of statistics and probability. … this is an interesting book which contains a lot of material.” (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2012 e)Table of ContentsPreface.- 1 Introduction and Overview.- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes integrals.- 3 Phi-variation and p-variation; Inequalities for Integrals.- 4 Banach Algebras.- 5 Derivatives and Analyticity in Normed Spaces.- 6 Nemytskii Operators on Function Spaces.- 7 Nemytskii Oerators on Lp Spaces.- 8 Two-Function Composition.- 9 Product Integration.- 10 Nonlinear Differential and Integral Equations.- 11 Fourier Series.- 12 Stochastic Processes and Phi-Variation.- Appendix Nonatomic Measure Spaces.- References.- Subject Index.- Author Index.- Index of Notation.
£123.49
Springer Analysis on Fock Spaces
Book SynopsisPreface.- Chapter 1. Preliminaries.- Chapter 2. Fock Spaces.- Chapter 3. The Berezin Transform and BMO.- Chapter 4. Interpolating and Sampling Sequences.- Chapter 5. Zero Sets for Fock Spaces.- Chapter 6. Toeplitz Operators.- Chapter 7. Small Hankel Operators.- Chapter 8. Hankel Operators.- References.- Index.Trade ReviewFrom the reviews:“Excellent books exist in the literature on the theory of Hardy spaces … but no textbook concerning the theory of Fock spaces has appeared before. The purpose of the author is to fill this gap and provide to any researcher in the field or graduate students the appropriate place to find the results or the bibliographical references needed for their use. … author succeeds with his goal. … a great addition to the literature and in the future will become a classic in the field.” (Jordi Pau, Mathematical Reviews, January, 2013)“This book is intended to provide a convenient reference to Fock spaces. … Each chapter ends with a series of exercises. The material is presented in a pedagogical way. The reference list contains 259 relevant items. This book is well written and it is a good reference for graduate students who are interested in Fock spaces.” (Atsushi Yamamori, Zentralblatt MATH, Vol. 1262, 2013)Table of ContentsPreface.- Chapter 1. Preliminaries.- Chapter 2. Fock Spaces.- Chapter 3. The Berezin Transform and BMO.- Chapter 4. Interpolating and Sampling Sequences.- Chapter 5. Zero Sets for Fock Spaces.- Chapter 6. Toeplitz Operators.- Chapter 7. Small Hankel Operators.- Chapter 8. Hankel Operators.- References.- Index.
£67.99
Springer-Verlag New York Inc. Fractal Geometry Complex Dimensions and Zeta
Book SynopsisIn its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.Trade Review“This interesting volume gives a thorough introduction to an active field of research and will be very valuable to graduate students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 180, 2016)“In this research monograph the authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner the results … are completely proved. I appreciate that the book is useful for mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying the fractals and dimension theory.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, April, 2013)“The authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner, the results (including some fundamental ones) are completely proved. … the book will be useful to mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying fractals and dimension theory.” (Nicolae-Adrian Secelean, Zentralblatt MATH, Vol. 1261, 2013)"In this book the author encompasses a broad range of topics that connect many areas of mathematics, including fractal geometry, number theory, spectral geometry, dynamical systems, complex analysis, distribution theory and mathematical physics. The book is self containing, the material organized in chapters preceding by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actual and has many applications." -- Nicolae-Adrian Secelean for Zentralblatt MATH"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style." -- Mathematical Reviews (Review of previous book by authors)"It is the reviewera (TM)s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced." -- Bulletin of the London Mathematical Society (Review of previous book by authors)"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics." -- Simulation News Europe (Review of previous book by authors)Table of ContentsPreface.- Overview.- Introduction.- 1. Complex Dimensions of Ordinary Fractal Strings.- 2. Complex Dimensions of Self-Similar Fractal Strings.- 3. Complex Dimensions of Nonlattice Self-Similar Strings.- 4. Generalized Fractal Strings Viewed as Measures.- 5. Explicit Formulas for Generalized Fractal Strings.- 6. The Geometry and the Spectrum of Fractal Strings.- 7. Periodic Orbits of Self-Similar Flows.- 8. Fractal Tube Formulas.- 9. Riemann Hypothesis and Inverse Spectral Problems.- 10. Generalized Cantor Strings and their Oscillations.- 11. Critical Zero of Zeta Functions.- 12 Fractality and Complex Dimensions.- 13. Recent Results and Perspectives.- Appendix A. Zeta Functions in Number Theory.- Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics.- Appendix C. An Application of Nevanlinna Theory.- Bibliography.- Author Index.- Subject Index.- Index of Symbols.- Conventions.- Acknowledgements.
£107.99
Springer-Verlag New York Inc. Ramanujans Lost Notebook Part IV
Book SynopsisIts discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.Table of ContentsPreface.- 1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manuscript on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta Functions adn Gauss Sums.- 15 Functional Equations for Products of Mellin Transforms.- 16 Infinite Products.- 17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt.- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis.- 20 Elementary Results.- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide.- Provenance.- References.- Index.
£116.99
Springer-Verlag New York Inc. Quantum Theory for Mathematicians
Book SynopsisAlthough ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book''s conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stonevon Neumann Theorem; the WentzelKramersBrillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basiTrade Review“This book is an introduction to quantum mechanics intended for mathematicians and mathematics students who do not have a particularly strong background in physics. … A well-qualified graduate student can learn a lot from this book. I found it to be clear and well organized, and I personally enjoyed reading it very much.” (David S. Watkins, SIAM Review, Vol. 57 (3), September, 2015)“This textbook is meant for advanced studies on quantum mechanics for a mathematical readership. The exercises at the end of each chapter make the book especially valuable.” (A. Winterhof, Internationale Mathematischen Nachrichten, Issue 228, 2015)“There are a few textbooks on quantum theory for mathematicians who are alien to the physical culture … but this modest textbook will surely find its place. All in all, the book is well written and accessible to any interested mathematicians and mathematical graduates.” (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)Table of Contents1 The Experimental Origins of Quantum Mechanics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schrödinger Equation.- 5 A Particle in a Square Well.- 6 Perspectives on the Spectral Theorem.- 7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements.- 8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs.- 9 Unbounded Self-Adjoint Operators.- 10 The Spectral Theorem for Unbounded Self-Adjoint Operators.- 11 The Harmonic Oscillator.- 12 The Uncertainty Principle.- 13 Quantization Schemes for Euclidean Space.- 14 The Stone–von Neumann Theorem.- 15 The WKB Approximation.- 16 Lie Groups, Lie Algebras, and Representations.- 17 Angular Momentum and Spin.- 18 Radial Potentials and the Hydrogen Atom.- 19 Systems and Subsystems, Multiple Particles.- V Advanced Topics in Classical and Quantum Mechanics.- 20 The Path-Integral Formulation of Quantum Mechanics.- 21 Hamiltonian Mechanics on Manifolds.- 22 Geometric Quantization on Euclidean Space.- 23 Geometric Quantization on Manifolds.- A Review of Basic Material.- References.- Index.
£56.69
Springer-Verlag New York Inc. Quadratic and Higher Degree Forms 31 Developments
Book SynopsisTable of ContentsPreface.- Toy Models for D. H. Lehmer's Conjecture II (E. Bannai, T. Miezaki).- On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich).- Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch).- Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Kominers).- Quadratic and Automorphic Forms (J. Hanke).- Integral Positive Ternary Quadratic Forms (W. Jagy).- Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala).- On the Length of Binary Forms (B. Reznick).- Representation of Quadratic Forms by Integral Quadratic Forms (R. Schulze-Pillot).- Identifying the Matrix Ring (J. Voight).
£95.99
Birkhauser Boston The Theory of Jacobi Forms 55 Progress in Mathematics
£110.49
MP-AMM American Mathematical Problems in Real and Functional Analysis
Book SynopsisTrade ReviewThe book is written in a very clear style and is very useful for graduate students to extend their vision of real and functional analysis."—Mohammad Sal Moslehian, Zentralblatt MATHTable of Contents Problems: Set theory and metric spaces Measures Lebesgue measure Measurable and integrable functions $L^p$ spaces Sequences of functions Product measures Normed linear spaces Functionals Normed linear spaces Linear operators Hilbert spaces Index
£108.00
MP-AMM American Mathematical Functional Analysis
Book SynopsisFunctional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate students and researchers. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a course on functional analysis for beginning graduate students.Table of Contents Foundations Principles of functional analysis The weak and weak* topologies Fredholm theory Spectral theory Unbounded operators Semigroups of operators Zorn and Tychonoff Bibliography Notation Index
£108.00
Springer New York Classical Fourier Analysis 2014
Book SynopsisThe coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition.Trade Review“The most up-to-date account of the most important developments in the area. … It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well” (Atanas G. Stefanov, Mathematical Reviews, August, 2015)Table of ContentsPreface.- 1. Lp Spaces and Interpolation.- 2. Maximal Functions, Fourier Transform, and Distributions.- 3. Fourier Series.- 4. Topics on Fourier Series.- 5. Singular Integrals of Convolution Type.- 6. Littlewood–Paley Theory and Multipliers.- 7. Weighted Inequalities.- A. Gamma and Beta Functions.- B. Bessel Functions.- C. Rademacher Functions.- D. Spherical Coordinates.- E. Some Trigonometric Identities and Inequalities.- F. Summation by Parts.- G. Basic Functional Analysis.- H. The Minimax Lemma.- I. Taylor's and Mean Value Theorem in Several Variables.- J. The Whitney Decomposition of Open Sets in Rn.- Glossary.- References.- Index.
£56.69
Springer-Verlag New York Inc. Free Probability and Random Matrices 35 Fields
Book SynopsisTrade Review“This book is an excellent survey, respectively introduction, into recent developments in free probability theory and its applications to random matrices. The authors superbly guide the reader through a number of important examples and present a carefully selected list of 207 relevant publications.” (Ludwig Paditz, zbMATH 1387.60005, 2018)Table of Contents1. Asymptotic Freeness of Gaussian Random Matrices.- 2. The Free Central Limit Theorem and Free Cumulants.- 3. Free Harmonic Analysis.- 4. Asymptotic Freeness.- 5. Second Order Freeness.- 6. Free Group Factors and Freeness.- 7. Free Entropy X-the Microstates Approach via Large Deviations.- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information.- 9. Operator-Valued Free Probability Theory and Block Random Matrices.- 10. Polynomials in Free Variables and Operator-Valued Convolution.- 11. Brown Measure.- Solutions to Exercises.- References.- Index of Exercises.
£107.99
Taylor & Francis Inc Exploring Calculus
Book SynopsisThis text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.Employs Mathematica to calculate and explore concepts and theories of calculusUses engaging labs to inspire learningIncludes many applications to a variety of fields that can promote research projectsUser-friendly approach that can be used for classroom work or independent exploratory leaTable of ContentsLimits and Continuity. Derivatives and Their Applications. Areas, Integrals, and Accumulation. Applications of Antiderivatives. Mathematica Demonstrations and References.
£35.99
Nova Science Publishers Inc Asymptotic Behavior: An Overview
Book SynopsisAsymptotic Behavior: An Overview is designed to provide the reader with an exposition of some aspects of the oscillation theory of first order delay partial dynamic equations on time scales. Oscillation theory of differential equations, originated from the monumental paper of C. Sturm published in 1836, has now been recognized as an important branch of mathematical analysis from both theoretical and practical viewpoints. Asymptotic behavior in the deep Euclidean region of momenta for four-dimensional models of quantum field theory is studied through the system of Schwinger-Dyson equations. This system is truncated by a sequence of n-particle approximations in which n → ∞ goes into the complete system of Schwinger-Dyson equations. Lastly, the authors discuss the exact analytical solution of the Schrödinger equation corresponding to the hydrogen atom confined by four spherical potentials: infinite potential, parabolic potential, constant potential, and dielectric continuum.
£58.39
Nova Science Publishers Inc Geometry of Linear 2Normed
Book Synopsis
£92.99
Nova Science Publishers Inc High Resolution Fourier Transform Spectroscopy of
Book SynopsisHigh resolution Fourier transform spectra of linear molecules have evoked a great deal of interest during the last several years, which could be seen from the several hundreds of papers published in the journal on the spectra of diatomic and small linear polyatomic molecules. This book describes the advantages of FT Spectroscopy, the techniques employed in absorption and emission spectroscopy, and presents the theoretical models and formulas used in the analyses and interpretation of the spectra. The Perturbations observed in the spectra due to Fermi, Darling-Dennison, Coriolis, and other anharmonic resonances; and vibrational and rotational l-type resonances etc. are discussed with suitable examples. The types of information obtained from FT spectroscopy of two to ten atomic linear molecules, their observed transitions and spectral perturbation etc. are presented along with figures and curves.
£43.49
Society for Industrial & Applied Mathematics,U.S. Extremum Seeking through Delays and PDEs
Book SynopsisExtremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find: Numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed. Extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided. The delays and pdes are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory. Accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.
£100.30
Nova Science Publishers Inc Nonlinear Functional Analysis & Applications:
Book Synopsis
£65.99
Nova Science Publishers Inc Nonlinear Functional Analysis & Applications:
Book Synopsis
£86.99
ISTE Ltd and John Wiley & Sons Inc Banach, Fréchet, Hilbert and Neumann Spaces
Book SynopsisThis book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.Table of ContentsIntroduction xi Familiarization with Semi-normed Spaces xv Notations xvii Chapter 1 Prerequisites 1 1.1 Sets, mappings, orders 1 1.2 Countability 3 1.3 Construction of R 4 1.4 Properties of R 5 Part 1 Semi-normed Spaces 9 Chapter 2 Semi-normed Spaces 11 2.1 Definition of semi-normed spaces 11 2.2 Convergent sequences 15 2.3 Bounded, open and closed sets 17 2.4 Interior, closure, balls and semi-balls 21 2.5 Density, separability 23 2.6 Compact sets 25 2.7 Connected and convex sets 30 Chapter 3 Comparison of Semi-normed Spaces 33 3.1 Equivalent families of semi-norms 33 3.2 Topological equalities and inclusions 34 3.3 Topological subspaces 39 3.4 Filtering families of semi-norms 43 3.5 Sums of sets 46 Chapter 4 Banach, Fréchet and Neumann Spaces 49 4.1 Metrizable spaces 49 4.2 Properties of sets in metrizable spaces 51 4.3 Banach, Fréchet and Neumann spaces 55 4.4 Compacts sets in Fréchet spaces 57 4.5 Properties of R 58 4.6 Convergent sequences 60 4.7 Sequential completion of a semi-normed space 62 Chapter 5 Hilbert Spaces 65 5.1 Hilbert spaces 65 5.2 Projection in a Hilbert space 68 5.3 The space Rd 70 Chapter 6 Product, Intersection, Sum and Quotient of Spaces 73 6.1 Product of semi-normed spaces 73 6.2 Product of a semi-normed space by itself 78 6.3 Intersection of semi-normed spaces 80 6.4 Sum of semi-normed spaces 83 6.5 Direct sum of semi-normed spaces 89 6.6 Quotient space 93 Part 2 Continuous Mappings 95 Chapter 7 Continuous Mappings 97 7.1 Continuous mappings 97 7.2 Continuity and change of topology or restriction 100 7.3 Continuity of composite mappings 102 7.4 Continuous semi-norms 102 7.5 Continuous linear mappings 104 7.6 Continuous multilinear mappings 107 7.7 Some continuous mappings 111 Chapter 8 Images of Sets Under Continuous Mappings 115 8.1 Images of open and closed sets 115 8.2 Images of dense, separable and connected sets 117 8.3 Images of compact sets 119 8.4 Images under continuous linear mappings 121 8.5 Continuous mappings in compact sets 123 8.6 Continuous real mappings 124 8.7 Compacting mappings 125 Chapter 9 Properties of Mappings in Metrizable Spaces 129 9.1 Continuous mappings in metrizable spaces 129 9.2 Banach’s fixed point theorem 133 9.3 Baire’s theorem 134 9.4 Open mapping theorem 136 9.5 Banach–Schauder’s continuity theorem 138 9.6 Closed graph theorem 139 Chapter 10 Extension of Mappings, Equicontinuity 141 10.1 Extension of equalities by continuity 141 10.2 Continuous extension of mappings 142 10.3 Equicontinuous families of mappings 146 10.4 Banach–Steinhaus equicontinuity theorem 148 Chapter 11 Compactness in Mapping Spaces 153 11.1 The spaces F(X; F) and C(X; F)-pt 153 11.2 Zorn’s lemma 154 11.3 Compactness in F(X; F) 157 11.4 An Ascoli compactness theorem in C(X; F)-pt 161 Chapter 12 Spaces of Linear or Multilinear Mappings 163 12.1 The space L(E; F) 163 12.2 Bounded sets in L(E; F) 165 12.3 Sequential completeness of L(E; F) when E is metrizable 167 12.4 Semi-norms and norm on L(E; F) when E isnormed 169 12.5 Continuity of the composition of linear mappings 171 12.6 Inversibility in the neighborhood of an isomorphism 174 12.7 The space Ld(E1 × ··· × Ed; F) 178 12.8 Separation of the variables of a multilinear mapping 181 Part 3 Weak Topologies 187 Chapter 13 Duality 189 13.1 Dual 189 13.2 Dual of a metrizable or normed space 193 13.3 Dual of a Hilbert space 196 13.4 Extraction of ∗ weakly converging subsequences 199 13.5 Continuity of the bilinear form of duality 203 13.6 Dual of a product 205 13.7 Dual of a direct sum 206 Chapter 14 Dual of a Subspace 209 14.1 Hahn–Banach theorem 209 14.2 Corollaries of the Hahn–Banach theorem 211 14.3 Characterization of a dense subspace 212 14.4 Dual of a subspace 213 14.5 Dual of an intersection 215 14.6 Dangerous identifications 216 Chapter 15 Weak Topology 221 15.1 Weak topology 221 15.2 Weak continuity and topological inclusions 224 15.3 Weak topology of a product 225 15.4 Weak topology of an intersection 226 15.5 Norm and semi-norms of a weak limit 228 Chapter 16 Properties of Sets for the Weak Topology 231 16.1 Banach–Mackey theorem (weakly bounded sets) 231 16.2 Gauge of a convex open set 233 16.3 Mazur’s theorem (weakly closed convex sets) 235 16.4 ˘Smulian’s theorem (weakly compact sets) 237 16.5 Semi-weak continuity of a bilinear mapping 240 Chapter 17 Reflexivity 243 17.1 Reflexive spaces 243 17.2 Sequential completion of a semi-reflexive space 247 17.3 Prereflexivity of metrizable spaces 248 17.4 Reflexivity of Hilbert spaces 250 17.5 Reflexivity of uniformly convex Banach spaces 252 17.6 A property of the combinations of linear forms 256 17.7 Characterizations of semi-reflexivity 257 17.8 Reflexivity of a subspace 261 17.9 Reflexivity of the image of a space 261 17.10 Reflexivity of the dual 263 Chapter 18 Extractable Spaces 265 18.1 Extractable spaces 265 18.2 Extractability of Hilbert spaces 266 18.3 Extractability of semi-reflexive spaces 267 18.4 Extractability of a subspace or of the image of a space 269 18.5 Extractability of a product or of a sum of spaces 270 18.6 Extractability of an intersection of spaces 271 18.7 Sequential completion of extractable spaces 271 Part 4 Differential Calculus 273 Chapter 19 Differentiable Mappings 275 19.1 Differentiable mappings 275 19.2 Differentiality, continuity and linearity 277 19.3 Differentiation and change of topology or restriction 279 19.4 Mean value theorem 281 19.5 Bounds on a real differentiable mapping 284 19.6 Differentiation of a composite mapping 286 19.7 Differential of an inverse mapping 289 19.8 Inverse mapping theorem 290 Chapter 20 Differentiation of Multivariable Mappings 295 20.1 Partial differentiation 295 20.2 Differentiation of a multilinear or multi-component mapping 298 20.3 Differentiation of a composite multilinear mapping 300 Chapter 21 Successive Differentiations 303 21.1 Successive differentiations 303 21.2 Schwarz’s symmetry principle 305 21.3 Successive differentiations of a composite mapping 308 Chapter 22 Derivation of Functions of One Real Variable 313 22.1 Derivative of a function of one real variable 313 22.2 Derivative of a real function of one real variable 315 22.3 Leibniz formula 319 22.4 Derivatives of the power, logarithm and exponential functions 320 Bibliography 325 Cited Authors 331 Index 335
£125.06
World Scientific Europe Ltd Friendly Approach To Functional Analysis, A
Book Synopsis'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
£88.20
World Scientific Europe Ltd Friendly Approach To Functional Analysis, A
Book Synopsis'The book is unusual among functional analysis books in devoting a lot of space to the derivative. The ‘friendly’ aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises.'MAA ReviewsThis book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
£53.20
World Scientific Europe Ltd D'oh! Fourier: Theory, Applications, And
Book SynopsisD'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively.The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.
£85.50
World Scientific Europe Ltd D'oh! Fourier: Theory, Applications, And
Book SynopsisD'oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively.The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D'oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.
£52.25
World Scientific Europe Ltd Modern Mathematical Methods For Scientists And
Book SynopsisModern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There is also an 'Application' section at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of 'put' and 'call' options in financial markets. The book presents several modern important and computationally efficient topics, including feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods.A unique and novel feature of the book is the introduction of a recently developed method for solving partial differential equations (PDEs), called the unified transform. PDEs are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics to ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge.The unified transform greatly facilitates this task. For example, two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, the unified transform derives in a simple manner a generalization of the d'Alembert solution, valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, the unified transform constructs a new solution to this ubiquitous PDE, with important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples.Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering.
£207.00
