Complex analysis, complex variables Books
Springer Verlag, Singapore Nevanlinna Theory
Book SynopsisThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.Table of ContentsPreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem4. Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applicationsReferences
£49.49
Springer Verlag, Singapore Mathematical Analysis and Applications: MAA 2020,
Book SynopsisThis book collects original peer-reviewed contributions presented at the "International Conference on Mathematical Analysis and Applications (MAA 2020)" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.Table of ContentsG. K. Srinivasan, A note on isolated removable singularities of harmonic functions.- O. Chadli, Ram N. Mohapatra, B. K. Sahu, Equilibrium Problems and Variational Inequalities: a Survey of Existence Results.- O. Chadli, Ram N. Mohapatra, G. Pany, Nonlinear evolution equations by a Ky Fan minimax inequality approach.- L. A. Wani and A. Swaminathan, Sufficient Conditions Concerning the Unified Class of Starlike and Convex Functions.- S. Menchavez and I. Mae Antabo, One Dimensional Parametrized Test Functions Space of Entire Functions.- D. Raghavan and S. Nagarajan, Extremal mild solutions of Hilfer fractional Impulsive systems.- B. Roy and S. N. Bora, On existence of integral solutions for a class of mixed Volterra-Fredholm integro fractional differential equations.- P. Kumar, A. Kumar, R. Kumar Vats and A. Kumar, Trajectory Controllability of Integro-differential Systems of Fractional Order γ ∈ (1, 2] in a Banach Space with Deviated Argument.- A. S. Kelil and A. Rao Appadu, Shehu-Adomian Decomposition Method for dispersive KdV-type Equations.- A. S. Kelil, A. R. Appadu and S. Arjika, On certain properties of perturbed Freud-type weight: a revisit.- A. K. Singh, Complex chaotic systems and its complexity.- M. Incesu, S. Y. Evren and O. Gursoy, On the bertrand pairs of open non uniform B-spline curves.- M. Verma, P. Sharma and N. Gupta, Convergence analysis of a sixth-order method under weak continuity condition with First-order Frechet derivative.- B. Kour and S. Ram, (m, n)-paranormal composition operators.- T. Yaying, On the domain of q-Euler matrix in c0 and c.- N. Sarkar and M. Sen, Study on some particular class of non linear integral equation with a hybridized approach.- D. Saha, M. Sen and S. Roy, Investigation of the existence criteria for the solution of the functional integral equation in the Lp space.- S. Das and K. Mehrez, Functional Inequalities for the Generalized Wright Functions.- S. Dutta and P. Guha, An Information Theoretic Entropy Related to Ihara $\zeta$ Function and Billiard Dynamics.- S. Baskaran, G. Saravanan and K. Muthunagai, On a new subclass of Sakaguchi type functions using (p;q)- derivative operator.- N. K. Jangid, S. Joshi and S. D. Purohit, Some Double integral Formulae Associated with Q Function and Galue Type Struve Function.- M. Jain, M. Singh and R. K. Meena, Time-dependent analytical and computational study of an M/M/1 queue with disaster failure and multiple working vacations.- M. Datta and N. Gupta, Usual stochastic ordering results for series and parallel systems with components having Exponentiated Chen distribution.
£104.99
Springer Verlag, Singapore Analytic Continuation and q-Convexity
Book SynopsisThe focus of this book is on the further development of the classical achievements in analysis of several complex variables, the analytic continuation and the analytic structure of sets, to settings in which the q-pseudoconvexity in the sense of Rothstein and the q-convexity in the sense of Grauert play a crucial role. After giving a brief survey of notions of generalized convexity and their most important results, the authors present recent statements on analytic continuation related to them. Rothstein (1955) first introduced q-pseudoconvexity using generalized Hartogs figures. Słodkowski (1986) defined q-pseudoconvex sets by means of the existence of exhaustion functions which are q-plurisubharmonic in the sense of Hunt and Murray (1978). Examples of q-pseudoconvex sets appear as complements of analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are q-pseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones. A similar generalization is obtained by a completely different approach using L²-methods in the setting of q-convex spaces. The notion of q-convexity was developed by Rothstein (1955) and Grauert (1959) and extended to q-convex spaces by Andreotti and Grauert (1962). Andreotti–Grauert's finiteness theorem was applied by Andreotti and Norguet (1966–1971) to extend Grauert's solution of the Levi problem to q-convex spaces. A consequence is that the sets of (q-1)-cycles of q-convex domains with smooth boundaries in projective algebraic manifolds, which are equipped with complex structures as open subsets of Chow varieties, are in fact holomorphically convex. Complements of analytic curves are studied, and the relation of q-convexity and cycle spaces is explained. Finally, results for q-convex domains in projective spaces are shown and the q-convexity in analytic families is investigated.Table of Contents1. Analytic Continuation and Pseudoconvexity.- 2. q-Plurisubharmonicity.- 3. q-Pseudoconvexity.- 4. q-Convexity and q-Completeness.- References.- Index.
£38.24
Springer Complex Geometric Analysis
Book Synopsis
£170.99
Taylor & Francis Ltd Real and Complex Analysis
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£58.89
Taylor & Francis Ltd An Introduction to Complex Analysis and the Laplace Transform
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£105.00
Cambridge University Press Intro to Hp Spaces 2ed 115 Cambridge Tracts in Mathematics Series Number 115
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£33.24
Cambridge University Press Spectral Thry Riemann ZetaFunction 127 Cambridge Tracts in Mathematics Series Number 127
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£49.39
Cambridge University Press Cauchy and the Creation of Complex Function Theory
Book SynopsisDr Smithies analyses the process whereby Cauchy created one of the most important branch of mathematics discovered in the nineteenth century. It is the first book to make use of the whole spectrum of available original sources, and will be recognised as the authoritative work on the creation of complex function theory.Trade ReviewReview of the hardback: 'This exemplary book is the first thorough and comprehensive presentation of Cauchy's creation between 1814 and 1831, of complex function theory … the papers form a diary that testifies to the gradual development of a new field in the mind of an outstanding mathematician.' D. Laugwitz, DarmstadtReview of the hardback: ' … an invaluable guide to anyone interested in the work of a great mathematician'. Jeremy Gray, The Open UniversityReview of the hardback: 'This book is a welcome contribution to the history of mathematical ideas. It is carefully written … in the case of a great mathematician of the first half of the nineteenth century, it is very useful to have a book analyzing his ideas. Smithie's book helps us understand the technical achievements of Cauchy in founding the theory of complex functions.' The Mathematical GazetteReview of the hardback: '… new light is thrown on Cauchy's thinking.' L'Enseignment MathématiqueReview of the hardback: '… a unique source not only for the historians of mathematics but to all who are fascinated by the beauty of the complex function theory.' European Mathematical SocietyTable of Contents1. Introduction; 2. The background to Cauchy's work on complex function theory; 3. Cauchy's 1814 memoir on definite integrals; 4. Miscellaneous contributions (1815–1825); 5. The 1825 memoir and associated papers; 6. The calculus of residues; 7. The Lagrange series and the Turin memoirs; 8. Summary and conclusions; References.
£44.64
Cambridge University Press Automorphic Forms on SL2 R Cambridge Tracts in Mathematics Series Number 130
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£48.44
Cambridge University Press Conformal Representation
Book SynopsisProfessor Carathéodory sets out the basic theory of conformal representations as simply as possible. In the early chapters on Mobius' and other elementary transformations and on non-Euclidean geometry, he deals with those elementary subjects that are necessary for an understanding of the general theory discussed in the remaining chapters.Table of Contents1. Mobius Transformation; 2. Non-Euclidean Geometry; 3. Elementary Transformations; 4. Schwarz's Lemma; 5. The Fundamental Theorems of Conformal Representation; 6. Transformation of the Frontier; 7. Transformation of Closed Surfaces; 8. The General Theorem of Uniformisation.
£35.14
Cambridge University Press Classical and Quantum Orthogonal Polynomials in One Variable 98 Encyclopedia of Mathematics and its Applications Series Number 98
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£73.30
Cambridge University Press Complex Variable Theory and Transform Calculus With Technical Applications
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£45.59
Cambridge University Press Several Complex Variables and Complex Manifolds II In Two Parts 66 London Mathematical Society Lecture Note Series Series Number 66
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£50.95
Cambridge University Press Complex Functions
Book SynopsisIn this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics.Trade Review"...a very nice treatment which emphasizes the unity of mathematics...Several years ago the reviewer wanted to teach an undergraduate course that gave an introduction to hyperbolic geometry, Möbius transformations and discrete groups. There was no suitable undergraduate text. This book fills that void," Mathematical Reviews"Well motivated with good selection of problems at the end of each chapter." American Mathematical Monthly"...clear and well written...Its message, admirably conveyed, is that mathematics is not a collection of neat parcels, the contents of one being blind to the contents of another." Times Higher Education Supplement"...clearly presented...a delightful book..." American ScientistTable of ContentsIntroduction; 1. The Riemann sphere; 2. Möbius transformations; 3. Elliptic functions; 4. Meromorphic continuation and Riemann surfaces; 5. PSL(2,R) and its discrete subgroups; 6. The modular group; Appendices; References; Index of symbols; Index of names and definitions.
£54.14
Cambridge University Press Spectral Theory of the Riemann ZetaFunction 127 Cambridge Tracts in Mathematics Series Number 127
Book SynopsisThe Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the develoTrade ReviewReview of the hardback: '… gives an excellent presentation of the interplay between the Riemann zeta function and automorphic forms … nicely written and of great interest for any number theorists.' R. Tichy, International Mathematical NewsTable of Contents1. Non-Euclidean harmonics; 2. Trace formulas; 3. Automorphic L-functions; 4. An explicit formula; 5. Asymptotics; References; Index.
£105.45
Cambridge University Press Potential Theory in the Complex Plane
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£47.49
Cambridge University Press LMS 199 Invariant Potential Theory London Mathematical Society Lecture Note Series Series Number 199
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£45.16
Cambridge University Press An Introduction to the Theory of the Riemann ZetaFunction 14 Cambridge Studies in Advanced Mathematics Series Number 14
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£46.54
Cambridge University Press Introduction to Compact Riemann Surfaces and Dessins dEnfants 79 London Mathematical Society Student Texts Series Number 79
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£100.70
Cambridge University Press Complex Variables Introduction and Applications Second Edition 35 Cambridge Texts in Applied Mathematics Series Number 35
Book SynopsisComplex variables provide powerful methods for attacking many difficult problems, and it is the aim of this book to provide a thorough grounding in these methods and their application. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate courses in complex variables.Trade Review'… an excellent text, and one of the most complete and well-written books on complex variables I have seen … The index is nicely composed, complete, and accurate … useful as a reference … I highly recommend it to anyone interested in the subject and have placed it prominently upon my reference bookshelf.' Duwayne Anderson, Optics and Photonics News'… an excellent text, and one of the most complete and well-written books on complex variables I have seen … I highly recommend it to anyone interested in the subject…'. Optics and Photonics News'Overall the book feels 'road-tested' both in the lecture theatre and in the crucible of research and the clear well-written text is complemented by a superb collection of worked examples and exercises ranging in scope from routine applications of techniques to more substantial illustrations of the theory.' The Mathematical Gazette'… the book is valuable for students in engineering and physical sciences.' ZAMMTable of ContentsPart I: 1. Complex numbers and elementary functions; 2. Analytic functions and integration; 3. Sequences, series and singularities of complex functions; 4. Residue calculus and applications of contour integration; Part II: 5. Conformal mapping and applications; 6. Asymptotic evaluation of integrals; 7. Riemann–Hilbert problems; Index.
£66.49
Cambridge University Press Singular Points of Plane Curves 63 London Mathematical Society Student Texts Series Number 63
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£65.54
Cambridge University Press Cauchy and the Creation of Complex Function Theory
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£105.45
Cambridge University Press Fundamentals of Hyperbolic Manifolds Selected Expositions London Mathematical Society Lecture Note Series Series Number 328
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£79.10
Cambridge University Press Complexity Hierarchical Structures Hierarchical Structures and Scaling in Physics 6 Cambridge Nonlinear Science Series Series Number 6
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£57.57
Cambridge University Press Heights in Diophantine Geometry 4 New Mathematical Monographs Series Number 4
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£62.69
Cambridge University Press Harmonic Measure New Mathematical Monographs Series Number 2
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£62.54
Cambridge University Press Geometry of Riemann Surfaces Proceedings of the Anogia Conference to Celebrate the 65th Birthday of William J Harvey 368 London Mathematical Society Lecture Note Series Series Number 368
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£55.91
Cambridge University Press Introduction to Compact Riemann Surfaces and Dessins dEnfants 79 London Mathematical Society Student Texts Series Number 79
Book SynopsisFew books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.Trade Review"Overall the text is very well written and easy to follow, partly due to the abundance of good concrete examples in every single section illustrating concepts from the very basic to the very technical." Aaron D. Wootton, Mathematical ReviewsTable of Contents1. Riemann surfaces and algebraic curves; 2. Riemann surfaces and Fuchsian groups; 3. Belyi's theorem; 4. Dessins d'enfants; References; Index.
£46.54
Cambridge University Press Several Complex Variables
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£151.05
Cambridge University Press Elliptic Functions 67 London Mathematical Society Student Texts Series Number 67
Book SynopsisThis 2006 treatment of Jacobi elliptic functions seeks to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' A rich variety of applications of the elliptic and related functions are also presented.Trade Review'This solid text is a good place to start when working with elliptic functions and it is the sort of book that you will keep coming back to as reference text.' Mathematics TodayTable of Contents1. The 'simple' pendulum; 2. Jacobian elliptic functions of a complex variable; 3. General properties of elliptic functions; 4. Theta functions; 5. The Jacobian elliptic functions for complex k; 6. Introduction to transformation theory; 7. The Weierstrass elliptic functions; 8. Elliptic integrals; 9. Applications of elliptic functions in geometry; 10. An application of elliptic functions in algebra solution of the general quintic equation; 11. An arithmetic application of elliptic functions; 12. Applications in mechanics and statistics and other topics; Appendix; Bibliography.
£166.25
Cambridge University Press Elliptic Functions 67 London Mathematical Society Student Texts Series Number 67
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£44.64
Cambridge University Press Characters and Automorphism Groups of Compact Riemann Surfaces 280 London Mathematical Society Lecture Note Series Series Number 280
Book SynopsisUsing modern methods from computational group theory and representation theory, this book addresses a classical topic in the theory of complex functions. It is suitable for graduate students and researchers.Trade Review'… by bringing together a number of very effective techniques, and by presenting a mass of specific evidence, Breuer has done the mathematical community a considerable service … the presentation of the material is excellent, with attractive layout … a valuable addition to the literature, which should be essential reading for anyone interested in the connections between Riemann surfaces and finite groups.' G. Jones, Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPreface; Notation; 1. Compact Riemann surfaces; 2. Group characters; 3. Automorphisms of compact Riemann surfaces; 4. Generation of groups; 5. Classification for small genus; 6. Classification for fixed group: real characters; 7. Classification for fixed group: nonreal irrationalities; Appendix A. Abelian inariants; Appendix B. Irreducible characters; Appendix C. Maillet's determinant; Bibliography; Index.
£57.57
Cambridge University Press Complex Analysis Cambridge Studies in Advanced
Book SynopsisWritten by a master of the subject, this text will be appreciated by students and experts for the way it develops the classical theory of functions of a complex variable in a clear and straightforward manner. In general, the approach taken here emphasises geometrical aspects of the theory in order to avoid some of the topological pitfalls associated with this subject. Thus, Cauchy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem, analytic functions on a Riemann surface, and ultimately the RiemannâRoch and Abel theorems. Profusely illustrated, and with plenty of examples, and problems (solutions to many of which are included), this book should be a stimulating text for advanced courses in complex analysis.Trade Review'While most of the material included in the first part could be used in a basic course on complex analysis, the whole book could serve as a text for an advanced course on Riemann surfaces. The book contains many pictures (helping to build geometric intuition) and problems (elementary and advanced). The book could be very helpful for students as well as for experts in the field.' European Mathematical Society NewsletterTable of Contents1. Holomorphic functions; 2. Cauchy's theorem; 3. Conformal mappings; 4. Analytic continuation; 5. Riemann's mapping theorem; 6. Riemann surfaces; 7. The structure of Riemann surfaces; 8. Analytic functions on a closed Riemann surface.
£69.34
Cambridge University Press An Introduction to Involutive Structures 6 New Mathematical Monographs Series Number 6
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£122.55
Cambridge University Press Equivalents of the Riemann Hypothesis Volume 3 Further Steps towards Resolving the Riemann Hypothesis
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£142.50
Cambridge University Press Numbers and Functions
Book SynopsisIn this updated edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn, progressing from experience through a structured sequence of over 800 problems to concepts, definitions and proofs of classical real analysis.Trade Review'This third edition of Numbers and Functions continues the author's long-term commitment to support every reader in making sense of mathematics by responding to a succession of well-chosen questions that encourage personal reflection and discussion with others. Groups of questions are followed by a summary to build the bigger picture. Every chapter includes details of the historical development and ends with a full list of solutions. The author is aware of the difficulties that students encounter with the complexity of the limit concept and begins with a pragmatic approach to null sequences. This broadens into a full study of limits of sequences, completeness, and a full range of tests for convergence of infinite series … This latest edition maintains the original chapters of the original, while benefiting from detailed improvements that have arisen from the experience of many readers. Thoroughly recommended.' David Tall, University of Warwick'… written in a very comprehensible but exact way … an excellent guide through the basic course of mathematical analysis at university.' European Mathematical Society NewsletterTable of ContentsPreface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. Inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completeness: mean value theorems, Taylor's Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index.
£44.64
McGraw-Hill Education - Europe Students Solutions Manual to accompany Complex
Book Synopsis
£216.24
