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Author: O.B. Bekken
Publisher: Springer
ISBN: 3540382011
Category : Mathematics
Languages : en
Pages : 216
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Book Description
Author: O.B. Bekken
Publisher: Springer
ISBN: 3540382011
Category : Mathematics
Languages : en
Pages : 216
Get Book Here
Book Description
Author: Kristian Seip
Publisher: American Mathematical Soc.
ISBN: 0821835548
Category : Mathematics
Languages : en
Pages : 153
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Book Description
Based 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
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: Robert C. Gunning
Publisher: American Mathematical Society
ISBN: 1470470667
Category : Mathematics
Languages : en
Pages : 334
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Book Description
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.
Author: Kenneth Hoffman
Publisher: Legare Street Press
ISBN: 9781015898240
Category :
Languages : en
Pages : 0
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Book Description
This 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.
Author: John Garnett
Publisher: Springer Science & Business Media
ISBN: 0387497633
Category : Mathematics
Languages : en
Pages : 471
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Book Description
This 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.
Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3319160591
Category : Mathematics
Languages : en
Pages : 523
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Book Description
This 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.
Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 048614996X
Category : Mathematics
Languages : en
Pages : 227
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Book Description
A 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.
Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
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Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author: Henri Cartan
Publisher: Courier Corporation
ISBN: 0486318672
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Basic 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.
