Two Problems In The Function Theory Of The Unit Ball Of Cn
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Two Problems In The Function Theory Of The Unit Ball Of Cn
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Author : Muddappa Seetharama Gowda
language : en
Publisher:
Release Date : 1982
Two Problems In The Function Theory Of The Unit Ball Of Cn written by Muddappa Seetharama Gowda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Two Problems In The Function Theory Of The Unit Ball Of
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Author : Muddappa Seetharama Gowda
language : en
Publisher:
Release Date : 1982
Two Problems In The Function Theory Of The Unit Ball Of written by Muddappa Seetharama Gowda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Holomorphic functions categories.
Function Theory In The Unit Ball Of Cn
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Author : W. Rudin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Function Theory In The Unit Ball Of Cn written by W. Rudin 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.
Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.
Harmonic And Subharmonic Function Theory On The Hyperbolic Ball
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Author : Manfred Stoll
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-30
Harmonic And Subharmonic Function Theory On The Hyperbolic Ball written by Manfred Stoll 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 2016-06-30 with Mathematics categories.
A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.
Geometric Function Theory In One And Higher Dimensions
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Author : Ian Graham
language : en
Publisher: CRC Press
Release Date : 2003-03-18
Geometric Function Theory In One And Higher Dimensions written by Ian Graham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-18 with Mathematics categories.
This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in
The Dirichlet Space And Related Function Spaces
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Author : Nicola Arcozzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-03
The Dirichlet Space And Related Function Spaces written by Nicola Arcozzi 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 2019-09-03 with Mathematics categories.
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Function Theory
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Author : Eric T. Sawyer
language : en
Publisher: American Mathematical Soc.
Release Date :
Function Theory written by Eric T. Sawyer 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 with Mathematics categories.
Function Theory In The Unit Ball Of Cn
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Author : Walter Rudin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Function Theory In The Unit Ball Of Cn written by Walter Rudin 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 2009-05-21 with Mathematics categories.
Function Theory in the Unit Ball of Cn. From the reviews: "...The book is easy on the reader. The prerequisites are minimal—just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. This presentation is unhurried and the author does most of the work. ...certainly a valuable reference book, and (even though there are no exercises) could be used as a text in advanced courses." R. Rochberg in Bulletin of the London Mathematical Society. "...an excellent introduction to one of the most active research fields of complex analysis. ...As the author emphasizes, the principal ideas can be presented clearly and explicitly in the ball, specific theorems can be quickly proved. ...Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined. ...Numerous examples throw light on the results as well as on the difficulties." C. Andreian Cazacu in Zentralblatt für Mathematik
New Constructions Of Functions Holomorphic In The Unit Ball Of Cn
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Author : Walter Rudin
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
New Constructions Of Functions Holomorphic In The Unit Ball Of Cn written by Walter Rudin 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 1986 with Mathematics categories.
The Madison Symposium On Complex Analysis
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Author : Edgar Lee Stout
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
The Madison Symposium On Complex Analysis written by Edgar Lee Stout 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 1992 with Mathematics categories.
This volume contains the proceedings of a Symposium on Complex Analysis, held at the University of Wisconsin at Madison in June 1991 on the occasion of the retirement of Walter Rudin. During the week of the conference, a group of about two hundred mathematicians from many nations gathered to discuss recent developments in complex analysis and to celebrate Rudin's long and productive career. Among the main subjects covered are applications of complex analysis to operator theory, polynomial convexity, holomorphic mappings, boundary behaviour of holomorphic functions, function theory on the unit disk and ball, and some aspects of the theory of partial differential equations related to complex analysis. Containing papers by some of the world's leading experts in these subjects, this book reports on current directions in complex analysis and presents an excellent mixture of the analytic and geometric aspects of the theory.