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Author: W. Rudin
Publisher: Springer Science & Business Media
ISBN: 1461380987
Category : Mathematics
Languages : en
Pages : 449
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Book Description
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.
Author: W. Rudin
Publisher: Springer Science & Business Media
ISBN: 1461380987
Category : Mathematics
Languages : en
Pages : 449
Get Book Here
Book Description
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.
Author: Walter Rudin
Publisher: American Mathematical Soc.
ISBN: 0821807137
Category : Mathematics
Languages : en
Pages : 96
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Book Description
Uses as a starting point A B Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C DEGREESn$. This title simplifies the construction of such functions by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of pr
Author: Carl H. FitzGerald
Publisher: World Scientific
ISBN: 9789812702500
Category : Mathematics
Languages : en
Pages : 360
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Book Description
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.
Author: Sheng Gong
Publisher: World Scientific
ISBN: 9814481912
Category : Mathematics
Languages : en
Pages : 353
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Book Description
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.
Author: Krzysztof Jarosz
Publisher: American Mathematical Soc.
ISBN: 0821832697
Category : Mathematics
Languages : en
Pages : 330
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Book Description
This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $Lp$-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented.
Author: Filippo Bracci
Publisher: Springer
ISBN: 3319731262
Category : Mathematics
Languages : en
Pages : 185
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Book Description
The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
Author: Ian Graham
Publisher: CRC Press
ISBN: 9780203911624
Category : Mathematics
Languages : en
Pages : 572
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Book Description
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
Author: Kehe Zhu
Publisher: Springer Science & Business Media
ISBN: 0387275398
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Can be used as a graduate text Contains many exercises Contains new results
Author: Carl C. Cowen Jr.
Publisher: Routledge
ISBN: 1351459139
Category : Mathematics
Languages : en
Pages : 404
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Book Description
The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.
Author: Nicola Arcozzi
Publisher: American Mathematical Soc.
ISBN: 0821839179
Category : Mathematics
Languages : en
Pages : 178
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Book Description
Contents: A tree structure for the unit ball $mathbb B? n$ in $mathbb C'n$; Carleson measures; Pointwise multipliers; Interpolating sequences; An almost invariant holomorphic derivative; Besov spaces on trees; Holomorphic Besov spaces on Bergman trees; Completing the multiplier interpolation loop; Appendix; Bibliography
