Topics In Complex Analysis
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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.
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
Topics In Complex Analysis And Operator Theory
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Author : Oscar Blasco
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Topics In Complex Analysis And Operator Theory written by Oscar Blasco 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 2012 with Mathematics categories.
This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.
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
A Course In Complex Analysis
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Author : Wolfgang Fischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-21
A Course In Complex Analysis written by Wolfgang Fischer 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 2011-10-21 with Mathematics categories.
This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.
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.
Selected Topics In Complex Analysis
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Author : Vladimir Ya. Eiderman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Selected Topics In Complex Analysis written by Vladimir Ya. Eiderman 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 2006-03-30 with Mathematics categories.
This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.
Topics In Complex Analysis
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Author : Mats Andersson
language : en
Publisher:
Release Date : 1996-11-15
Topics In Complex Analysis written by Mats Andersson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-15 with categories.
Complex Analysis
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Author : Shashank Tiwari
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Complex Analysis written by Shashank Tiwari and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Complex Analysis: Advanced Concepts" delves into the intricate world of complex numbers and functions, offering a thorough exploration of their properties and applications. The book begins with a detailed examination of basic concepts, covering arithmetic operations, geometric interpretations, and the fundamental theorem of algebra. It then progresses to advanced topics such as complex functions, differentiation, integration, and series. One of the book's notable strengths lies in its clear and concise explanations, accompanied by numerous examples and exercises to reinforce understanding. Readers are guided through theorems and proofs, gaining insight into the elegance and power of complex analysis. The book also highlights the relevance of complex analysis in various fields, including physics, engineering, and economics. Applications such as potential theory, fluid dynamics, and signal processing are explored, demonstrating the subject's practical significance. Whether used as a textbook for students or a reference for professionals, "Complex Analysis: Advanced Concepts" offers a valuable resource for mastering the intricacies of this essential branch of mathematics. Its comprehensive coverage and accessible style make it an indispensable addition to any mathematician's library.
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.