Boundary Behavior Of Holomorphic Functions Of Several Complex Variables Mn 11
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Boundary Behavior Of Holomorphic Functions Of Several Complex Variables Mn 11
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Boundary Behavior Of Holomorphic Functions Of Several Complex Variables Mn 11 written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.
This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Boundry Behvior Of Holomorphic Functions Of Several
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Author : Elias M. Stein
language : en
Publisher:
Release Date : 1972
Boundry Behvior Of Holomorphic Functions Of Several written by Elias M. Stein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Boundary Behavior Of Holomorphic Functions
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Author : Fausto Di Biase
language : en
Publisher: Birkhauser
Release Date : 2006-10
Boundary Behavior Of Holomorphic Functions written by Fausto Di Biase and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10 with Mathematics categories.
This monograph examines the boundary behavior of holomorphic functions in several complex variables. Moving beyond the early ideas of Fatou and others, Koranyi and then Stein in the late 1960s and early 1970s deepened the study of Fatou-type theorems in several complex variables, showing that in a general context, approach regions of a shape dramatically larger than non-tangential will give rise to a Fatou-type theorem. These have become known as the admissible regions of Koranyi and Stein. It turns out, however, that the admissible approach regions are only optimal on strongly pseudoconvex domains. Considerable effort has been made in the last 20 years to adapt Fatou theory, and the approach regions in particular, to the Levi geometry of a given domain in multidimensional complex space. The work of Di Biase in the late 1990s is devoted to the Nagel--Stein phenomenon, describing a more general notion of approach region that supersedes the classical ideas of non-tangential and admissible. Krantz's work Function Theory of Several Complex Variables (2000), still the only introduction to the subject, focuses on methods based on maximal function estimates. To date, the main open problem, which is the special focus of this book, is the issue of determining the {it optimal natural approach regions} for the almost everywhere convergence to the boundary of certain smoothly bounded pseudoconvex domains. This book provides the proper framework for the eventual solution of the main problem. This work gives an updated, comprehensive, and self-contained exposition of many results that have never appeared in book form. Starting with foundational material, i.e., from the unit disc in one complexvariable, the reader is lead to the latest discoveries in higher dimensions. New results in boundary value issues of holomorphic functions are examined, which in turn point to new open problems. The book may be used by analysts for individual study or by graduate students.
Several Complex Variables
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Author : Joseph John Kohn
language : en
Publisher:
Release Date : 1984
Several Complex Variables written by Joseph John Kohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Functions of several complex variables categories.
"These papers, originally presented at the first international conference in several complex variables held in China, cover complex differential geometry, integral representation, boundary behavior of holomorphic functions, invariant metrics, holomorphic vector bundles, and pseudoconvexity."--Publisher.
Beijing Lectures In Harmonic Analysis Am 112 Volume 112
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Beijing Lectures In Harmonic Analysis Am 112 Volume 112 written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.
Complex Analysis
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Author : Steven George Krantz
language : en
Publisher: Springer
Release Date : 1987
Complex Analysis written by Steven George Krantz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
This conference gathered together a small group of people with similar interests in the geometric function theory of several complex variables. While the speeches were of a specialized nature, the papers in the proceedings are largely of a survey and speculative nature. The volume is intended to serve both students and researchers as an invitation to active new areas of research. The level of the writing has been intentionally set in such a way that the papers will be accessible to a broad audience.
Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Normal Families And Normal Functions
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Author : Peter V. Dovbush
language : en
Publisher:
Release Date : 2024
Normal Families And Normal Functions written by Peter V. Dovbush and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Mathematics categories.
This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.
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.
Algebraic Structures Of Symmetric Domains
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Author : Ichiro Satake
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Algebraic Structures Of Symmetric Domains written by Ichiro Satake and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.