Function Theory In The Unit Ball Of Cn

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Function Theory in the Unit Ball of Cn

Author : W. Rudin
Publisher : Springer Science & Business Media
ISBN 13 : 1461380987
Total Pages : 449 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Function Theory in the Unit Ball of Cn by : W. Rudin

Download or read book Function Theory in the Unit Ball of Cn written by W. Rudin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Function Theory in the Unit Ball of Cn

Author :
Publisher :
ISBN 13 : 9787510052699
Total Pages : 436 pages
Book Rating : 4.0/5 (526 download)

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Book Synopsis Function Theory in the Unit Ball of Cn by :

Download or read book Function Theory in the Unit Ball of Cn written by and published by . This book was released on 1980 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:

New Constructions of Functions Holomorphic in the Unit Ball of CN

Author : Walter Rudin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889084
Total Pages : 100 pages
Book Rating : 4.8/5 (89 download)

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Book Synopsis New Constructions of Functions Holomorphic in the Unit Ball of CN by : Walter Rudin

Download or read book New Constructions of Functions Holomorphic in the Unit Ball of CN written by Walter Rudin and published by American Mathematical Soc.. This book was released on 1986 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Invariant Potential Theory in the Unit Ball of Cn

Author : Manfred Stoll
Publisher : Cambridge University Press
ISBN 13 : 0521468302
Total Pages : 187 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Invariant Potential Theory in the Unit Ball of Cn by : Manfred Stoll

Download or read book Invariant Potential Theory in the Unit Ball of Cn written by Manfred Stoll and published by Cambridge University Press. This book was released on 1994-05-12 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

Two Problems in the Function Theory of the Unit Ball of Ǹ

Author : Muddappa Seetharama Gowda
Publisher :
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Two Problems in the Function Theory of the Unit Ball of Ǹ by : Muddappa Seetharama Gowda

Download or read book Two Problems in the Function Theory of the Unit Ball of Ǹ written by Muddappa Seetharama Gowda and published by . This book was released on 1982 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Function Theory in Several Complex Variables

Author : Carl H. FitzGerald
Publisher : World Scientific
ISBN 13 : 9789812702500
Total Pages : 360 pages
Book Rating : 4.7/5 (25 download)

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Book Synopsis Geometric Function Theory in Several Complex Variables by : Carl H. FitzGerald

Download or read book Geometric Function Theory in Several Complex Variables written by Carl H. FitzGerald and published by World Scientific. This book was released on 2004 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

Author : Manfred Stoll
Publisher : Cambridge University Press
ISBN 13 : 1107541484
Total Pages : 243 pages
Book Rating : 4.1/5 (75 download)

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Book Synopsis Harmonic and Subharmonic Function Theory on the Hyperbolic Ball by : Manfred Stoll

Download or read book Harmonic and Subharmonic Function Theory on the Hyperbolic Ball written by Manfred Stoll and published by Cambridge University Press. This book was released on 2016-06-30 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.

Spaces of Holomorphic Functions in the Unit Ball

Author : Kehe Zhu
Publisher : Springer Science & Business Media
ISBN 13 : 0387275398
Total Pages : 281 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Spaces of Holomorphic Functions in the Unit Ball by : Kehe Zhu

Download or read book Spaces of Holomorphic Functions in the Unit Ball written by Kehe Zhu and published by Springer Science & Business Media. This book was released on 2006-03-22 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can be used as a graduate text Contains many exercises Contains new results

Geometric Function Theory in Higher Dimension

Author : Filippo Bracci
Publisher : Springer
ISBN 13 : 3319731262
Total Pages : 182 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Geometric Function Theory in Higher Dimension by : Filippo Bracci

Download or read book Geometric Function Theory in Higher Dimension written by Filippo Bracci and published by Springer. This book was released on 2018-03-24 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Analytic Function Spaces and their Applications

Author : Javad Mashreghi
Publisher : Springer Nature
ISBN 13 : 3031335724
Total Pages : 426 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Lectures on Analytic Function Spaces and their Applications by : Javad Mashreghi

Download or read book Lectures on Analytic Function Spaces and their Applications written by Javad Mashreghi and published by Springer Nature. This book was released on 2023-11-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.

Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Author : Manuel Cepedello Boiso
Publisher : Springer Science & Business Media
ISBN 13 : 3034806485
Total Pages : 535 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation by : Manuel Cepedello Boiso

Download or read book Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation written by Manuel Cepedello Boiso and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.

Composition Operators on Spaces of Analytic Functions

Author : Carl C. Cowen Jr.
Publisher : Routledge
ISBN 13 : 1351459139
Total Pages : 404 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Composition Operators on Spaces of Analytic Functions by : Carl C. Cowen Jr.

Download or read book Composition Operators on Spaces of Analytic Functions written by Carl C. Cowen Jr. and published by Routledge. This book was released on 2019-03-04 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Dirichlet Space and Related Function Spaces

Author : Nicola Arcozzi
Publisher : American Mathematical Soc.
ISBN 13 : 1470450828
Total Pages : 536 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Dirichlet Space and Related Function Spaces by : Nicola Arcozzi

Download or read book The Dirichlet Space and Related Function Spaces written by Nicola Arcozzi and published by American Mathematical Soc.. This book was released on 2019-09-03 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Function Theory in Several Complex Variables

Author : Carl H FitzGerald
Publisher : World Scientific
ISBN 13 : 9814481912
Total Pages : 352 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric Function Theory in Several Complex Variables by : Carl H FitzGerald

Download or read book Geometric Function Theory in Several Complex Variables written by Carl H FitzGerald and published by World Scientific. This book was released on 2004-09-23 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Subriemannian Geometry and Subelliptic Partial Differential Equations (D-C Chang et al.)Proper Holomorphic Mappings between Some Generalized Hartogs Triangles (Z Chen)Invariant Mappings in Geometric Function Theory (C H FitzGerald)The Distortion Theorems for Convex Mappings in Several Complex Variables (S Gong)Basic Properties of Loewner Chains in Several Complex Variables (I Graham et al.)A New Inequality and Its Applications (H Ke)Intermediate Value Theorem for Functions of Classes of Riemann Surfaces (M Masumoto)A Hadamard Theorem on Algebraic Curves (S-K Wang & H-P Zhang)Hodge-Laplace Operator on Complex Finsler Manifolds (C Zhong & T Zhong)and other papers Readership: Graduate students, researchers and academics in mathematics. Keywords:Geometric Function Theory;Several Complex Variables;Function Theory;Holomorlphic Mappings;Subriemannian Geometry;Riemann Manifolds;Finsler Manifolds;Loewner ChainsKey Features:Written to be understood and to be used by a wide audienceContains survey papers on important areas of research mathematicsWritten by mathematicians of international stature

Finite or Infinite Dimensional Complex Analysis

Author : Joji Kajiwara
Publisher : CRC Press
ISBN 13 : 1482270595
Total Pages : 656 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Finite or Infinite Dimensional Complex Analysis by : Joji Kajiwara

Download or read book Finite or Infinite Dimensional Complex Analysis written by Joji Kajiwara and published by CRC Press. This book was released on 2019-05-07 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.

Handbook of the Geometry of Banach Spaces

Author :
Publisher : Elsevier
ISBN 13 : 9780080533506
Total Pages : 870 pages
Book Rating : 4.5/5 (335 download)

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Book Synopsis Handbook of the Geometry of Banach Spaces by :

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces

Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces

Author : Miroljub Jevtić
Publisher : Springer
ISBN 13 : 331945644X
Total Pages : 323 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces by : Miroljub Jevtić

Download or read book Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces written by Miroljub Jevtić and published by Springer. This book was released on 2016-12-24 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic overview of the theory of Taylor coefficients of functions in some classical spaces of analytic functions and especially of the coefficient multipliers between spaces of Hardy type. Offering a comprehensive reference guide to the subject, it is the first of its kind in this area. After several introductory chapters covering the basic material, a large variety of results obtained over the past 80 years, including the most recent ones, are treated in detail. Several chapters end with discussions of practical applications and related topics that graduate students and experts in other subjects may find useful for their own purposes. Thus, a further aim of the book is to communicate to non-specialists some concrete facts that may be of value in their own work. The book can also be used as a textbook or a supplementary reference for an advanced graduate course. It is primarily intended for specialists in complex and functional analysis, graduate students, and experts in other related fields.