Functional analysis and transforms Books
Cambridge University Press LMS 137 Analysis at Urbana Volume 1 Volume 1 Analysis in Function Spaces London Mathematical Society Lecture Note Series Series Number 137
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£80.76
Cambridge University Press Volterra Integral and Functional Equations 34 Encyclopedia of Mathematics and its Applications Series Number 34
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£152.95
Cambridge University Press Heat Kernels and Spectral Theory
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£49.39
Cambridge University Press Absolutely Summing Operators 43 Cambridge Studies in Advanced Mathematics Series Number 43
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£95.95
Cambridge University Press Exercises in Fourier Analysis
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£53.19
Cambridge University Press Ergodic Theory and Harmonic Analysis Proceedings of the 1993 Alexandria Conference 205 London Mathematical Society Lecture Note Series Series Number 205
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£58.40
Cambridge University Press Multivalent Functions 110 Cambridge Tracts in Mathematics Series Number 110
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£105.45
Cambridge University Press Geometric Applications of Fourier Series and Spherical Harmonics
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£105.45
Cambridge University Press Dynamics of Linear Operators 179 Cambridge Tracts in Mathematics Series Number 179
Book SynopsisThe first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.Trade Review'The beginning of each chapter sets the stage for what is to follow and each concludes with detailed comments, notes, references and a carefully selected list of problems. These serve the reader well, providing historical motivation as well as resources for further work … the book … is well developed, the material is well motivated and the selected topics that are explained include original results along with important simplifications of proofs from the existing research literature. The book has an extensive list of references covering the topics discussed, making it an excellent guide for students of the subject … this well-written book is a valuable resource for anyone working in Operator Theory, but is also accessible to anyone with a reasonable background in functional analysis at the graduate level.' Mathematical ReviewsTable of ContentsIntroduction; 1. Hypercyclic and supercyclic operators; 2. Hypercyclicity everywhere; 3. Connectedness and hypercyclicity; 4. Weakly mixing operators; 5. Ergodic theory and linear dynamics; 6. Beyond hypercyclicity; 7. Common hypercyclic vectors; 8. Hypercyclic subspaces; 9. Supercyclicity and the angle criterion; 10. Linear dynamics and the weak topology; 11. Universality of the Riemann zeta function; 12. About 'the' Read operator; Appendices; Notations; Index; Bibliography.
£78.84
Cambridge University Press Introduction to Banach Algebras Operators and Harmonic Analysis 57 London Mathematical Society Student Texts Series Number 57
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£52.24
Cambridge University Press Func Anly Prob Stoch Processes
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£62.69
Cambridge University Press An Introduction to Harmonic Analysis
Book SynopsisFirst published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. This new edition has been revised by the author, to include several new sections and a new appendix.Trade Review'… the third, revised, edition … Katznelson managed to improve on a seemingly perfect book!' Nieuw Archif voor WiskundeTable of Contents1. Fourier series on T; 2. The convergence of Fourier series; 3. The conjugate function; 4. Interpolation of linear operators; 5. Lacunary series and quasi-analytic classes; 6. Fourier transforms on the line; 7. Fourier analysis on locally compact Abelian groups; 8. Commutative Banach algebras; A. Vector-valued functions; B. Probabilistic methods.
£42.74
Cambridge University Press A Mathematical Introduction to Wavelets 37 London Mathematical Society Student Texts Series Number 37
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£100.70
Cambridge University Press A Mathematical Introduction to Wavelets
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£48.44
Cambridge University Press Automorphic Forms on SL2 R 130 Cambridge Tracts in Mathematics Series Number 130
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£105.45
Cambridge University Press LMS 234 Introduction to Subfactors London Mathematical Society Lecture Note Series Series Number 234
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£72.48
Cambridge University Press Fourier Series and Integral Transforms
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£94.99
Cambridge University Press Fourier Series and Integral Transforms
Book SynopsisThis book's aim is to provide the reader with a basic understanding of Fourier series and transforms, and Laplace transforms. It is based on the authors' notes for a one semester course. Prerequisites are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with exercises and examples of applications.Trade Review"With its frequent examples and exercises, the present book is eminently suitable for both self-study and a one-semester course." ChoiceTable of Contents1. Notation and terminology; 2. Background: inner product spaces; 3. Fourier series; 4. Fourier transforms; 5. The Laplace transform; Appendices.
£38.94
Cambridge University Press A Short Course on Banach Space Theory 64 London Mathematical Society Student Texts Series Number 64
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£38.94
Cambridge University Press Fredholm Theory in Banach Spaces
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£44.64
Cambridge University Press Holomorphic Spaces 33 Mathematical Sciences Research Institute Publications Series Number 33
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£133.95
Cambridge University Press A Practical Guide to Pseudospectral Methods
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£39.89
Cambridge University Press Dirac Operators Spectral Geometry 12 Cambridge Lecture Notes in Physics Series Number 12
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£42.74
Cambridge University Press Geometry of Sets Measures Spaces Fractals and Rectifiability 44 Cambridge Studies in Advanced Mathematics Series Number 44
Book SynopsisNow in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.Trade Review"Provides a unified theory for the study of the topic and develops the main tools used in its study including theorems, Hausdorff measures, and their relations to Riesz capacities and Fourier transforms." Book News, Inc.Table of ContentsAcknowledgements; Basic notation; Introduction; 1. General measure theory; 2. Covering and differentiation; 3. Invariant measures; 4. Hausdorff measures and dimension; 5. Other measures and dimensions; 6. Density theorems for Hausdorff and packing measures; 7. Lipschitz maps; 8. Energies, capacities and subsets of finite measure; 9. Orthogonal projections; 10. Intersections with planes; 11. Local structure of s-dimensional sets and measures; 12. The Fourier transform and its applications; 13. Intersections of general sets; 14. Tangent measures and densities; 15. Rectifiable sets and approximate tangent planes; 16. Rectifiability, weak linear approximation and tangent measures; 17. Rectifiability and densities; 18. Rectifiability and orthogonal projections; 19. Rectifiability and othogonal projections; 19. Rectifiability and analytic capacity in the complex plane; 20. Rectifiability and singular intervals; References; List of notation; Index of terminology.
£72.19
Cambridge University Press Automorphic Forms Representations 55 Cambridge Studies in Advanced Mathematics Series Number 55
Book SynopsisIntermediate in level between an advanced textbook and a monograph, this book covers both the classical and representation theoretic views of automorphic forms in a style which is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the RankinâSelberg method and the triple L-function, examining this subject matter from many different and complementary viewpoints. Researchers as well as students will find this a valuable guide to a notoriously difficult subject.Trade Review'This important textbook closes a gap in the existing literature, for it presents the 'representation theoretic' viewpoint of the theory of automorphic forms on GL(2) … it will become a stepping stone for many who want to study the Corvallis Proceedings or the Lecture Notes by H. Jaquet and R. Langlands or seek a pathway to R. Langland's conjectures.' Monatshefte für Mathematik'Students and researchers will find the book an understandable and penetrating treatment of a beautiful theory.' European Mathematical SocietyTable of Contents1. Modular forms; 2. Automorphic forms and representations of GL( 2, R); 3. Automorphic representations; 4. GL(2) over a p-adic field.
£56.99
Cambridge University Press An Introduction to Functional Analysis
Book SynopsisThis text covers key results in functional analysis that are essential for further study in analysis, the calculus of variations, dynamical systems, and the theory of partial differential equations. More than 200 fully-worked exercises and detailed proofs are given, making this ideal for upper undergraduate and beginning graduate courses.Trade Review'This excellent introduction to functional analysis brings the reader at a gentle pace from a rudimentary acquaintance with analysis to a command of the subject sufficient, for example, to start a rigorous study of partial differential equations. The choice and order of topics are very well thought-out, and there is a fine balance between general results and concrete examples and applications.' Charles Fefferman, Princeton University, New Jersey'An Introduction to Functional Analysis covers everything that one would expect to meet in an undergraduate course on this elegant area and more, including spectral theory, the category-based theorems and unbounded operators. With a well-written narrative and clear detailed proofs, together with plentiful examples and exercises, this is both an excellent course book and a valuable reference for those encountering functional analysis from across mathematics and science.' Kenneth Falconer, University of St Andrews, Scotland'This is a beautifully written book, containing a wealth of worked examples and exercises, covering the core of the theory of Banach and Hilbert spaces. The book will be of particular interest to those wishing to learn the basic functional analytic tools for the mathematical analysis of partial differential equations and the calculus of variations.' Endre Suli, University of Oxford'… this is a valuable book. It is an accessible yet serious look at the subject, and anybody who has worked through it will be rewarded with a good understanding of functional analysis, and should be in a position to read more advanced books with profit.' Mark Hunacek, The Mathematical GazetteTable of ContentsPart I. Preliminaries: 1. Vector spaces and bases; 2. Metric spaces; Part II. Normed Linear Spaces: 3. Norms and normed spaces; 4. Complete normed spaces; 5. Finite-dimensional normed spaces; 6. Spaces of continuous functions; 7. Completions and the Lebesgue spaces Lp(Ω); Part III. Hilbert Spaces: 8. Hilbert spaces; 9. Orthonormal sets and orthonormal bases for Hilbert spaces; 10. Closest points and approximation; 11. Linear maps between normed spaces; 12. Dual spaces and the Riesz representation theorem; 13. The Hilbert adjoint of a linear operator; 14. The spectrum of a bounded linear operator; 15. Compact linear operators; 16. The Hilbert–Schmidt theorem; 17. Application: Sturm–Liouville problems; Part IV. Banach Spaces: 18. Dual spaces of Banach spaces; 19. The Hahn–Banach theorem; 20. Some applications of the Hahn–Banach theorem; 21. Convex subsets of Banach spaces; 22. The principle of uniform boundedness; 23. The open mapping, inverse mapping, and closed graph theorems; 24. Spectral theory for compact operators; 25. Unbounded operators on Hilbert spaces; 26. Reflexive spaces; 27. Weak and weak-* convergence; Appendix A. Zorn's lemma; Appendix B. Lebesgue integration; Appendix C. The Banach–Alaoglu theorem; Solutions to exercises; References; Index.
£33.24
Cambridge University Press Singular Perturbations of Differential Operators Solvable Schrdingertype Operators 271 London Mathematical Society Lecture Note Series Series Number 271
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£61.71
Cambridge University Press Wavelets CaldernZygmund and Multilinear Operators 48 Cambridge Studies in Advanced Mathematics Series Number 48
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£72.19
Cambridge University Press Introduction to Operator Space Theory
Book SynopsisAn introduction to the theory of operator spaces, emphasising examples that illustrate the theory and applications to C*-algebras, and applications to non self-adjoint operator algebras, and similarity problems. Postgraduate and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find the book has much to offer.Trade Review'The tone of the book is quite informal, friendly and inviting. Even to experts in the field, a large proportion of the results, and certainly of the proofs, will be new and stimulating. … there are literally thousands of wonderful results and insights in the text which the reader will not find elsewhere. The book covers an incredible amount of ground, and makes use of some of the most exciting recent work in modern analysis. … It is a magnificent book: an enormous treasure trove, and a work of love and care by one of the great analysts of our time. All students and researchers in functional analysis should have a copy. Anybody planning to work in operator space theory will need to be thoroughly immersed in it.' Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPart I. Introduction to Operator Spaces: 1. Completely bounded maps; 2. Minimal tensor product; 3. Minimal and maximal operator space structures on a Banach space; 4. Projective tensor product; 5. The Haagerup tensor product; 6. Characterizations of operator algebras; 7. The operator Hilbert space; 8. Group C*-algebras; 9. Examples and comments; 10. Comparisons; Part II. Operator Spaces and C*-tensor products: 11. C*-norms on tensor products; 12. Nuclearity and approximation properties; 13. C*; 14. Kirchberg's theorem on decomposable maps; 15. The weak expectation property; 16. The local lifting property; 17. Exactness; 18. Local reflexivity; 19. Grothendieck's theorem for operator spaces; 20. Estimating the norms of sums of unitaries; 21. Local theory of operator spaces; 22. B(H) * B(H); 23. Completely isomorphic C*-algebras; 24. Injective and projective operator spaces; Part III. Operator Spaces and Non Self-Adjoint Operator Algebras: 25. Maximal tensor products and free products of non self-adjoint operator algebras; 26. The Blechter-Paulsen factorization; 27. Similarity problems; 28. The Sz-nagy-halmos similarity problem; Solutions to the exercises; References.
£87.99
Cambridge University Press Introduction to Banach Algebras Operators and Harmonic Analysis 57 London Mathematical Society Student Texts Series Number 57
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£111.15
Cambridge University Press Functional Analysis for Probability and Stochastic Processes An Introduction
Book SynopsisThis text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.Trade Review"My impression is that this text might well succeed as an attractive introduction to, or even as propaganda for the subject of probability and stochastic processes for a well-educated analyst without a probabilistic background." N.H. Bingham, Journal of the American Statistical AssociationTable of ContentsPreface; 1. Preliminaries, notations and conventions; 2. Basic notions in functional analysis; 3. Conditional expectation; 4. Brownian motion and Hilbert spaces; 5. Dual spaces and convergence of probability measures; 6. The Gelfand transform and its applications; 7. Semigroups of operators and Lévy processes; 8. Markov processes and semigroups of operators; 9. Appendixes; References; Index.
£133.95
Cambridge University Press An Introduction to Harmonic Analysis
Book SynopsisFirst published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. This new edition has been revised by the author, to include several new sections and a new appendix.Trade Review'… the third, revised, edition … Katznelson managed to improve on a seemingly perfect book!' Nieuw Archif voor WiskundeTable of Contents1. Fourier series on T; 2. The convergence of Fourier series; 3. The conjugate function; 4. Interpolation of linear operators; 5. Lacunary series and quasi-analytic classes; 6. Fourier transforms on the line; 7. Fourier analysis on locally compact Abelian groups; 8. Commutative Banach algebras; A. Vector-valued functions; B. Probabilistic methods.
£116.85
Cambridge University Press A Short Course on Banach Space Theory
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£133.95
Cambridge University Press Introduction to Radon Transforms
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£151.05
Cambridge University Press Functional Integration
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£147.25
Cambridge University Press Core Science 1 Key Concepts
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£60.79
Cambridge University Press An Introduction to Functional Analysis
Book SynopsisThis accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the HilbertSchmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the HahnBanach theorem, the KreinMilman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and begTrade Review'This excellent introduction to functional analysis brings the reader at a gentle pace from a rudimentary acquaintance with analysis to a command of the subject sufficient, for example, to start a rigorous study of partial differential equations. The choice and order of topics are very well thought-out, and there is a fine balance between general results and concrete examples and applications.' Charles Fefferman, Princeton University, New Jersey'An Introduction to Functional Analysis covers everything that one would expect to meet in an undergraduate course on this elegant area and more, including spectral theory, the category-based theorems and unbounded operators. With a well-written narrative and clear detailed proofs, together with plentiful examples and exercises, this is both an excellent course book and a valuable reference for those encountering functional analysis from across mathematics and science.' Kenneth Falconer, University of St Andrews, Scotland'This is a beautifully written book, containing a wealth of worked examples and exercises, covering the core of the theory of Banach and Hilbert spaces. The book will be of particular interest to those wishing to learn the basic functional analytic tools for the mathematical analysis of partial differential equations and the calculus of variations.' Endre Suli, University of Oxford'… this is a valuable book. It is an accessible yet serious look at the subject, and anybody who has worked through it will be rewarded with a good understanding of functional analysis, and should be in a position to read more advanced books with profit.' Mark Hunacek, The Mathematical GazetteTable of ContentsPart I. Preliminaries: 1. Vector spaces and bases; 2. Metric spaces; Part II. Normed Linear Spaces: 3. Norms and normed spaces; 4. Complete normed spaces; 5. Finite-dimensional normed spaces; 6. Spaces of continuous functions; 7. Completions and the Lebesgue spaces Lp(Ω); Part III. Hilbert Spaces: 8. Hilbert spaces; 9. Orthonormal sets and orthonormal bases for Hilbert spaces; 10. Closest points and approximation; 11. Linear maps between normed spaces; 12. Dual spaces and the Riesz representation theorem; 13. The Hilbert adjoint of a linear operator; 14. The spectrum of a bounded linear operator; 15. Compact linear operators; 16. The Hilbert–Schmidt theorem; 17. Application: Sturm–Liouville problems; Part IV. Banach Spaces: 18. Dual spaces of Banach spaces; 19. The Hahn–Banach theorem; 20. Some applications of the Hahn–Banach theorem; 21. Convex subsets of Banach spaces; 22. The principle of uniform boundedness; 23. The open mapping, inverse mapping, and closed graph theorems; 24. Spectral theory for compact operators; 25. Unbounded operators on Hilbert spaces; 26. Reflexive spaces; 27. Weak and weak-* convergence; Appendix A. Zorn's lemma; Appendix B. Lebesgue integration; Appendix C. The Banach–Alaoglu theorem; Solutions to exercises; References; Index.
£71.24
Cambridge University Press Recent Developments in Algebraic Geometry
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£57.00
Cambridge University Press Fractional Sobolev Spaces and Inequalities
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£90.25
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.
£57.94
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.
£22.18
Cambridge University Press Representations of Solvable Lie Groups
Book SynopsisThe theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.Trade Review'There is … the included background material on Lie theory, and there are also quite a lot of examples provided. Aspiring researchers in this area will likely find these features helpful, both aspiring and current researchers should also appreciate the wealth of material found here, as well as the extensive (five page, 92 entries) bibliography.' Mark Hunacek, MAA Reviews'… embeddings into matrix algebras and unitary representations are both possible and useful, and they are given a central role in this book.' M. Bona, Choice'Throughout the book, the authors carefully explain the theory step by step and provide many concrete examples with computations which help the readers to understand. This book is a valuable exposition and an excellent research guide for the basic representation theory of solvable Lie groups for graduate students and researchers.' Junko Inoue, MathSciNet'This monograph is a summary of a long career and experience of two great experts in their domain. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers. The concrete and example-based exposition is accessible to advanced graduate students and non-specialists.' Béchir Dali, zbMATHTable of Contents1. Basic theory of solvable Lie algebras and Lie groups; 2. Stratification of an orbit space; 3. Unitary representations; 4. Coadjoint orbits and polarizations; 5. Irreducible unitary representations; 6. Plancherel formula and related topics; List of notations; Bibliography; Index.
£133.94
