Introduction To Geometric Function Theory Of Hypercomplex Variables
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Introduction To Geometric Function Theory Of Hypercomplex Variables
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Author : Sorin G. Gal
language : en
Publisher: Nova Publishers
Release Date : 2002
Introduction To Geometric Function Theory Of Hypercomplex Variables written by Sorin G. Gal and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Introduction to Geometric Function Theory of Hypercomplex Variables
Several Complex Variables Iii
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Author : G.M. Khenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Several Complex Variables Iii written by G.M. Khenkin 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.
We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
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 Functions of several complex variables 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 : Carl Hanson FitzGerald
language : en
Publisher: World Scientific
Release Date : 2004
Geometric Function Theory In Several Complex Variables written by Carl Hanson FitzGerald and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.
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.
Regular Functions Of A Quaternionic Variable
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Author : Graziano Gentili
language : en
Publisher: Springer Nature
Release Date : 2022-09-23
Regular Functions Of A Quaternionic Variable written by Graziano Gentili and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-23 with Mathematics categories.
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
Bicomplex Holomorphic Functions
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Author : M. Elena Luna-Elizarrarás
language : en
Publisher: Birkhäuser
Release Date : 2015-12-11
Bicomplex Holomorphic Functions written by M. Elena Luna-Elizarrarás and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-11 with Mathematics categories.
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable. While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a “complexification” of the field of complex numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one- or multidimensional complex analysis.
Advances In Complex Analysis And Operator Theory
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Author : Fabrizio Colombo
language : en
Publisher: Birkhäuser
Release Date : 2017-09-30
Advances In Complex Analysis And Operator Theory written by Fabrizio Colombo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-30 with Mathematics categories.
This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.
Several Complex Variables And Complex Geometry Part Iii
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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Several Complex Variables And Complex Geometry Part Iii written by Eric Bedford 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 1991 with Mathematics categories.
Geometric Theory Of Functions Of A Complex Variable
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Author : G. M. Goluzin
language : en
Publisher:
Release Date :
Geometric Theory Of Functions Of A Complex Variable written by G. M. Goluzin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Functions of complex variables categories.
This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long.