Topics In Complex Analysis
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Topics In Complex Analysis
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Author : Mats Andersson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In Complex Analysis written by Mats Andersson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is an outgrowth of lectures given on several occasions at Chalmers University of Technology and Goteborg University during the last ten years. As opposed to most introductory books on complex analysis, this one as sumes that the reader has previous knowledge of basic real analysis. This makes it possible to follow a rather quick route through the most fundamen tal material on the subject in order to move ahead to reach some classical highlights (such as Fatou theorems and some Nevanlinna theory), as well as some more recent topics (for example, the corona theorem and the HI_ BMO duality) within the time frame of a one-semester course. Sections 3 and 4 in Chapter 2, Sections 5 and 6 in Chapter 3, Section 3 in Chapter 5, and Section 4 in Chapter 7 were not contained in my original lecture notes and therefore might be considered special topics. In addition, they are completely independent and can be omitted with no loss of continuity. The order of the topics in the exposition coincides to a large degree with historical developments. The first five chapters essentially deal with theory developed in the nineteenth century, whereas the remaining chapters contain material from the early twentieth century up to the 1980s. Choosing methods of presentation and proofs is a delicate task. My aim has been to point out connections with real analysis and harmonic anal ysis, while at the same time treating classical complex function theory.
Topics In Complex Analysis
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Author : Dan Romik
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-08-21
Topics In Complex Analysis written by Dan Romik and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-21 with Mathematics categories.
This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 — a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
Complex Analysis
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Author : Mario Gonzalez
language : en
Publisher: Routledge
Release Date : 2018-03-09
Complex Analysis written by Mario Gonzalez and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Mathematics categories.
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
Complex Analysis And Special Topics In Harmonic Analysis
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Author : Carlos A. Berenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis And Special Topics In Harmonic Analysis written by Carlos A. Berenstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
Some Topics In Complex Analysis
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Author : Edgar Giraldus Phillips
language : en
Publisher:
Release Date : 1966
Some Topics In Complex Analysis written by Edgar Giraldus Phillips and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Electronic books categories.
Some Topics in Complex Analysis.
Topics In Complex Analysis
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Author : Dorothy Brown Shaffer
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Topics In Complex Analysis written by Dorothy Brown Shaffer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Presents mathematical ideas based on papers given at an AMS meeting held at Fairfield University in October 1983. This work deals with the Loewner equation, classical results on coefficient bodies and modern optimal control theory. It also deals with support points for the class $S$, Loewner chains and the process of truncation.
Topics In Complex Analysis
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Author : Dan Romik
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-08-21
Topics In Complex Analysis written by Dan Romik and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-21 with Mathematics categories.
This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 -- a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
Complex Analysis
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Author : Andrei Bourchtein
language : en
Publisher: Springer Nature
Release Date : 2021-02-09
Complex Analysis written by Andrei Bourchtein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-09 with Mathematics categories.
This book discusses all the major topics of complex analysis, beginning with the properties of complex numbers and ending with the proofs of the fundamental principles of conformal mappings. Topics covered in the book include the study of holomorphic and analytic functions, classification of singular points and the Laurent series expansion, theory of residues and their application to evaluation of integrals, systematic study of elementary functions, analysis of conformal mappings and their applications—making this book self-sufficient and the reader independent of any other texts on complex variables. The book is aimed at the advanced undergraduate students of mathematics and engineering, as well as those interested in studying complex analysis with a good working knowledge of advanced calculus. The mathematical level of the exposition corresponds to advanced undergraduate courses of mathematical analysis and first graduate introduction to the discipline. The book contains a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic skills and test the understanding of concepts. Other problems are more theoretically oriented and illustrate intricate points of the theory. Many additional problems are proposed as homework tasks whose level ranges from straightforward, but not overly simple, exercises to problems of considerable difficulty but of comparable interest.
Classical Topics In Complex Function Theory
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Author : Reinhold Remmert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Classical Topics In Complex Function Theory written by Reinhold Remmert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike
Current Topics In Pure And Computational Complex Analysis
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Author : Santosh Joshi
language : en
Publisher: Springer
Release Date : 2014-12-02
Current Topics In Pure And Computational Complex Analysis written by Santosh Joshi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
The book contains 13 articles, some of which are survey articles and others research papers. Written by eminent mathematicians, these articles were presented at the International Workshop on Complex Analysis and Its Applications held at Walchand College of Engineering, Sangli. All the contributing authors are actively engaged in research fields related to the topic of the book. The workshop offered a comprehensive exposition of the recent developments in geometric functions theory, planar harmonic mappings, entire and meromorphic functions and their applications, both theoretical and computational. The recent developments in complex analysis and its applications play a crucial role in research in many disciplines.