The Geometric Theory Of Complex Variables
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Geometric Theory Of Functions Of A Complex Variable
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Author : Gennadiĭ Mikhaĭlovich Goluzin
language : en
Publisher: American Mathematical Soc.
Release Date : 1969
Geometric Theory Of Functions Of A Complex Variable written by Gennadiĭ Mikhaĭlovich Goluzin 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 1969 with Functions of complex variables categories.
The Geometric Theory Of Complex Variables
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Author : Peter V. Dovbush
language : en
Publisher: Springer Nature
Release Date : 2025-01-28
The Geometric Theory Of Complex Variables written by Peter V. Dovbush and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.
This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.
Function Theory Of Several Complex Variables
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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory Of Several Complex Variables written by Steven George Krantz 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 2001 with Mathematics categories.
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Geometric Function Theory In Several Complex Variables
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Author : Junjirō Noguchi
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Geometric Function Theory In Several Complex Variables written by Junjirō Noguchi 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 1990 with Mathematics categories.
This is an expanded English-language version of a book by the same authors that originally appeared in the Japanese. The book serves two purposes. The first is to provide a self-contained and coherent account of recent developments in geometric function theory in several complex variables, aimed at those who have already mastered the basics of complex function theory and the elementary theory of differential and complex manifolds. The second goal is to present, in a self-contained way, fundamental descriptions of the theory of positive currents, plurisubharmonic functions, and meromorphic mappings, which are today indispensable in the analytic and geometric theories of complex functions of several variables. The book should prove useful for researchers and graduate students alike.
Complex Analysis
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Author : Steven G. Krantz
language : en
Publisher: Cambridge University Press
Release Date : 2004
Complex Analysis written by Steven G. Krantz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
In this second edition of a Carus Monograph Classic, Steven Krantz develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disc. He also introduces the Bergman kernel and metric and provides profound applications, some of them never having appeared before in print. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. This is the first and only book to describe the context, the background, the details, and the applications of Ahlfors's celebrated ideas about curvature, the Schwarz lemma, and applications in complex analysis. Beginning from scratch, and requiring only a minimal background in complex variable theory, this book takes the reader up to ideas that are currently active areas of study. Such areas include a) the Caratheodory and Kobayashi metrics, b) the Bergman kernel and metric, c) boundary continuation of conformal maps. There is also an introduction to the theory of several complex variables. Poincar 's celebrated theorem about the biholomorphic inequivalence of the ball and polydisc is discussed and proved.
Theory Of Complex Functions
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Author : Reinhold Remmert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Complex Functions 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 2012-12-06 with Mathematics categories.
A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Analytic Functions Of Several Complex Variables
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Author : Robert Clifford Gunning
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Analytic Functions Of Several Complex Variables written by Robert Clifford Gunning 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 2009 with Mathematics categories.
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Representation Theory And Complex Analysis
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Author : Michael Cowling
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-27
Representation Theory And Complex Analysis written by Michael Cowling 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 2008-02-27 with Mathematics categories.
Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Complex Variables
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2007-09-19
Complex Variables written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-19 with Mathematics categories.
From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, MapleTM, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences.