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Author | : Carl C. Cowen Jr. |
Publisher | : Routledge |
Total Pages | : 404 |
Release | : 2019-03-04 |
Genre | : Mathematics |
ISBN | : 1351459139 |
Download Composition Operators on Spaces of Analytic Functions Book in PDF, ePub and Kindle
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 | : Carl C. Cowen, Jr. |
Publisher | : Routledge |
Total Pages | : 401 |
Release | : 2019-03-04 |
Genre | : Mathematics |
ISBN | : 1351459147 |
Download Composition Operators on Spaces of Analytic Functions Book in PDF, ePub and Kindle
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 | : Joel H. Shapiro |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208874 |
Download Composition Operators Book in PDF, ePub and Kindle
The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.
Author | : R.K. Singh |
Publisher | : Elsevier |
Total Pages | : 327 |
Release | : 1993-11-03 |
Genre | : Mathematics |
ISBN | : 0080872905 |
Download Composition Operators on Function Spaces Book in PDF, ePub and Kindle
This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.
Author | : Rocky Mountain Mathematics Consortium |
Publisher | : American Mathematical Soc. |
Total Pages | : 266 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821807684 |
Download Studies on Composition Operators Book in PDF, ePub and Kindle
This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on "Composition Operators on Spaces of Analytic Functions" held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.
Author | : Kehe Zhu |
Publisher | : CRC Press |
Total Pages | : 228 |
Release | : 2019-05-10 |
Genre | : Mathematics |
ISBN | : 1351045539 |
Download Handbook of Analytic Operator Theory Book in PDF, ePub and Kindle
This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators
Author | : Kehe Zhu |
Publisher | : American Mathematical Soc. |
Total Pages | : 368 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821839659 |
Download Operator Theory in Function Spaces Book in PDF, ePub and Kindle
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Author | : Lixin Zheng |
Publisher | : |
Total Pages | : 72 |
Release | : 2000 |
Genre | : Analytic functions |
ISBN | : |
Download The Essential Norm and Spectrum of Composition Operators on Space of Bounded Analytic Functions Book in PDF, ePub and Kindle
Author | : Alexandru Aleman |
Publisher | : Birkhäuser |
Total Pages | : 281 |
Release | : 2020-08-15 |
Genre | : Mathematics |
ISBN | : 9783030146429 |
Download Analysis of Operators on Function Spaces Book in PDF, ePub and Kindle
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.
Author | : Xiangling Zhu |
Publisher | : |
Total Pages | : 152 |
Release | : 2017-05-18 |
Genre | : |
ISBN | : 9783330088726 |
Download Generalized Weighted Composition Operators on Analytic Function Spaces Book in PDF, ePub and Kindle