Spaces of Analytic Functions
Author: O.B. Bekken
Publisher: Springer
Published: 2006-11-14
Total Pages: 216
ISBN-13: 3540382011
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Interpolation and Sampling in Spaces of Analytic Functions
Author: Kristian Seip
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 153
ISBN-13: 0821835548
DOWNLOAD EBOOKBased on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an
Composition Operators on Spaces of Analytic Functions
Author: Carl C. Cowen Jr.
Publisher: Routledge
Published: 2019-03-04
Total Pages: 404
ISBN-13: 1351459139
DOWNLOAD EBOOKThe 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.
Analytic Functions of Several Complex Variables
Author: Robert Clifford Gunning
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 338
ISBN-13: 0821821652
DOWNLOAD EBOOKThe theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Bounded Analytic Functions
Author: John Garnett
Publisher: Springer Science & Business Media
Published: 2007-04-05
Total Pages: 471
ISBN-13: 0387497633
DOWNLOAD EBOOKThis book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.
Banach Spaces Of Analytic Functions
Author: Kenneth Hoffman
Publisher: Legare Street Press
Published: 2022-10-27
Total Pages: 0
ISBN-13: 9781015898240
DOWNLOAD EBOOKThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Banach Spaces of Analytic Functions
Author: Kenneth Hoffman
Publisher: Courier Corporation
Published: 2014-06-10
Total Pages: 227
ISBN-13: 048614996X
DOWNLOAD EBOOKA classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc. The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the factorization, and a brief description of the classical approach to the theorems of the first five chapters. The remainder of the book addresses the structure of various Banach spaces and Banach algebras of analytic functions in the unit disc. Enhanced with 100 challenging exercises, a bibliography, and an index, this text belongs in the libraries of students, professional mathematicians, as well as anyone interested in a rigorous, high-level treatment of this topic.
An Advanced Complex Analysis Problem Book
Author: Daniel Alpay
Publisher: Birkhäuser
Published: 2015-11-13
Total Pages: 523
ISBN-13: 3319160591
DOWNLOAD EBOOKThis is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
Elementary Theory of Analytic Functions of One or Several Complex Variables
Author: Henri Cartan
Publisher: Courier Corporation
Published: 2013-04-22
Total Pages: 242
ISBN-13: 0486318672
DOWNLOAD EBOOKBasic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Analysis on Fock Spaces
Author: Kehe Zhu
Publisher: Springer Science & Business Media
Published: 2012-05-26
Total Pages: 350
ISBN-13: 1441988017
DOWNLOAD EBOOKSeveral natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.
