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Nine Introductions in Complex Analysis

Nine Introductions in Complex Analysis
A Book

by Sanford L. Segal

  • Publisher : Elsevier
  • Release : 2011-08-18
  • Pages : 714
  • ISBN : 9780080871646
  • Language : En, Es, Fr & De
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Nine Introductions in Complex Analysis

Nine Introductions in Complex Analysis, Revised Edition

Nine Introductions in Complex Analysis, Revised Edition
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2008
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Nine Introductions in Complex Analysis - Revised Edition

Nine Introductions in Complex Analysis - Revised Edition
A Book

by Sanford L. Segal

  • Publisher : Elsevier
  • Release : 2007-10-10
  • Pages : 500
  • ISBN : 9780080550763
  • Language : En, Es, Fr & De
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The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off

A Quick Introduction to Complex Analysis

A Quick Introduction to Complex Analysis
A Book

by Kalyan Chakraborty,Shigeru Kanemitsu,Takako Kuzumaki

  • Publisher : World Scientific Publishing Company
  • Release : 2016-08-08
  • Pages : 208
  • ISBN : 9813108533
  • Language : En, Es, Fr & De
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The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels. If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples. This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

by Barry Simon

  • Publisher : American Mathematical Soc.
  • Release : 2015-11-02
  • Pages : 641
  • ISBN : 1470411008
  • Language : En, Es, Fr & De
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A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

A Complex Analysis Problem Book

A Complex Analysis Problem Book
A Book

by Daniel Alpay

  • Publisher : Birkhäuser
  • Release : 2016-10-26
  • Pages : 596
  • ISBN : 3319421816
  • Language : En, Es, Fr & De
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This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

An Advanced Complex Analysis Problem Book

An Advanced Complex Analysis Problem Book
Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

by Daniel Alpay

  • Publisher : Birkhäuser
  • Release : 2015-11-13
  • Pages : 521
  • ISBN : 3319160591
  • Language : En, Es, Fr & De
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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Complex Analysis

Complex Analysis
Selected Topics

by Mario Gonzalez

  • Publisher : Routledge
  • Release : 2018-03-09
  • Pages : 544
  • ISBN : 1351459384
  • Language : En, Es, Fr & De
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A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Fourier Analysis with Applications

Fourier Analysis with Applications
A Book

by Adrian Constantin

  • Publisher : Cambridge University Press
  • Release : 2016-06-02
  • Pages : 368
  • ISBN : 1107044103
  • Language : En, Es, Fr & De
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A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.

Elliptic Curves

Elliptic Curves
Function Theory, Geometry, Arithmetic

by Henry McKean,Victor Moll

  • Publisher : Cambridge University Press
  • Release : 1999-08-13
  • Pages : 280
  • ISBN : 9780521658171
  • Language : En, Es, Fr & De
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An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.

A History of Complex Dynamics

A History of Complex Dynamics
From Schröder to Fatou and Julia

by Daniel S. Alexander

  • Publisher : Springer Science & Business Media
  • Release : 2013-06-29
  • Pages : 166
  • ISBN : 366309197X
  • Language : En, Es, Fr & De
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The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.

Early Days in Complex Dynamics

Early Days in Complex Dynamics
A History of Complex Dynamics in One Variable During 1906-1942

by Daniel S. Alexander,Felice Iavernaro,Alessandro Rosa

  • Publisher : American Mathematical Soc.
  • Release : 2012
  • Pages : 454
  • ISBN : 0821844644
  • Language : En, Es, Fr & De
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The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book by Alexander, Iavernaro, and Rosa paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others. A recurrent theme of the authors' treatment is the center problem in complex dynamics. They present its complete history during this period and, in so doing, bring out analogies between complex dynamics and the study of differential equations, in particular, the problem of stability in Hamiltonian systems. Among these analogies are the use of iteration and problems involving small divisors which the authors examine in the work of Poincare and others, linking them to complex dynamics, principally via the work of Samuel Lattes, in the early 1900s, and Jurgen Moser, in the 1960s. Many details will be new to the reader, such as a history of Lattes functions (functions whose Julia set equals the Riemann sphere), complex dynamics in the United States around the time of World War I, a survey of complex dynamics around the world in the 1920s and 1930s, a discussion of the dynamical programs of Fatou and Julia during the 1920s, and biographical material on several key figures. The book contains graphical renderings of many of the mathematical objects the authors discuss, including some of the intriguing fractals Fatou and Julia studied, and concludes with several appendices by current researchers in complex dynamics which collectively attest to the impact of the work of Fatou, Julia, and others upon the present-day study.

Normal Families

Normal Families
A Book

by Joel L. Schiff

  • Publisher : Springer Science & Business Media
  • Release : 1993-03-25
  • Pages : 236
  • ISBN : 9780387979670
  • Language : En, Es, Fr & De
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A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in

Dynamics: Topology and Numbers

Dynamics: Topology and Numbers
A Book

by Pieter Moree,Anke Pohl,L’ubomír Snoha,Tom Ward

  • Publisher : American Mathematical Soc.
  • Release : 2020-02-12
  • Pages : 347
  • ISBN : 147045100X
  • Language : En, Es, Fr & De
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This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.

Hidden Harmony—Geometric Fantasies

Hidden Harmony—Geometric Fantasies
The Rise of Complex Function Theory

by Umberto Bottazzini,Jeremy Gray

  • Publisher : Springer Science & Business Media
  • Release : 2013-06-21
  • Pages : 848
  • ISBN : 1461457254
  • Language : En, Es, Fr & De
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​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Radical Banach Algebras and Automatic Continuity

Radical Banach Algebras and Automatic Continuity
Proceedings of a Conference Held at California State University Long Beach, July 17-31, 1981

by J.M. Bachar,W.G. Bade,P.C. Jr. Curtis,H.G. Dales,M.P. Thomas

  • Publisher : Springer
  • Release : 2006-11-15
  • Pages : 470
  • ISBN : 3540394540
  • Language : En, Es, Fr & De
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Vector-Valued Functions and their Applications

Vector-Valued Functions and their Applications
A Book

by Chuang-Gan Hu,Chung-Chun Yang

  • Publisher : Springer Science & Business Media
  • Release : 2013-04-17
  • Pages : 160
  • ISBN : 9401580308
  • Language : En, Es, Fr & De
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This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. The book contains three chapters devoted to the theory of normal functions, Hp-space, and vector-valued functions and their applications. Among the topics dealt with are the properties of complex functions in a complex plane and infinite-dimensional spaces, and the solution of vector-valued integral equations and boundary value problems by complex analysis and functional analysis, which involve methods which can be applied to problems in operations research and control theory. Much original research is included. This volume will be of interest to those whose work involves complex analysis and control theory, and can be recommended as a graduate text in these areas.

Additive Number Theory

Additive Number Theory
Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson

by David Chudnovsky,Gregory Chudnovsky

  • Publisher : Springer Science & Business Media
  • Release : 2010-08-26
  • Pages : 361
  • ISBN : 9780387683614
  • Language : En, Es, Fr & De
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This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.

Spectral Theory of Canonical Systems

Spectral Theory of Canonical Systems
A Book

by Christian Remling

  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 2018-08-21
  • Pages : 206
  • ISBN : 3110563231
  • Language : En, Es, Fr & De
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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Mathematics Unbound

Mathematics Unbound
The Evolution of an International Mathematical Research Community, 1800-1945

by Karen Hunger Parshall,Adrian Clifford Rice

  • Publisher : American Mathematical Soc.
  • Release : 2021
  • Pages : 406
  • ISBN : 9780821896730
  • Language : En, Es, Fr & De
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Although today's mathematical research community takes its international character very much for granted, this ''global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.