Studies On Composition Operators
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Studies On Composition Operators
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Author : Rocky Mountain Mathematics Consortium
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Studies On Composition Operators written by Rocky Mountain Mathematics Consortium and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Studies On Composition Operators And Function Spaces
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Author : Marko Kotilainen
language : en
Publisher:
Release Date : 2007
Studies On Composition Operators And Function Spaces written by Marko Kotilainen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Composition operators categories.
This survey part of the thesis contains some background to the series of studies on composition operators and function spaces. Bounded and compact composition operators are studied in analytic Qk type spaces and in some real function spaces. So-called Bloch-Sobolev spaces are introduced. An asymptotic formula for the essential norm of the composition operator mapping into Qk(p,q) is established. Carleson measures are studied in higher dimensions and used in the study of hyperbolic harmonic function spaces. A short summary of the articles is included.
Composition Operators On Spaces Of Analytic Functions
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Author : Carl C. Cowen Jr.
language : en
Publisher: Routledge
Release Date : 2019-03-04
Composition Operators On Spaces Of Analytic Functions written by Carl C. Cowen Jr. and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-04 with Mathematics categories.
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.
Composition Operators
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Author : Joel H. Shapiro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Composition Operators written by Joel H. Shapiro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Composition Operators On Function Spaces
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Author : R.K. Singh
language : en
Publisher: Elsevier
Release Date : 1993-11-03
Composition Operators On Function Spaces written by R.K. Singh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-03 with Mathematics categories.
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.
Problems And Recent Methods In Operator Theory
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Author : Fernanda Botelho
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-18
Problems And Recent Methods In Operator Theory written by Fernanda Botelho and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Mathematics categories.
This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Nonlinear Superposition Operators
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Author : Jurgen Appell
language : en
Publisher: Cambridge University Press
Release Date : 1990
Nonlinear Superposition Operators written by Jurgen Appell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Aiming to present a self-contained account of the present state of knowledge of the theory of the non-linear superposition operators - a generalization of the notion of functions - this book diverges from classical nonlinear analysis and is applicable to operators in a variety of function spaces.
Absolutely Summing Operators
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Author : Joe Diestel
language : en
Publisher: Cambridge University Press
Release Date : 1995-04-27
Absolutely Summing Operators written by Joe Diestel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Mathematics categories.
This text provides the beginning graduate student with an account of p-summing and related operators.
Advanced Courses Of Mathematical Analysis Vi Proceedings Of The Sixth International School
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Author : Francisco Javier Martin-reyes
language : en
Publisher: World Scientific
Release Date : 2016-10-27
Advanced Courses Of Mathematical Analysis Vi Proceedings Of The Sixth International School written by Francisco Javier Martin-reyes and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-27 with Mathematics categories.
This volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.
Classical Descriptive Set Theory
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Author : Alexander Kechris
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Descriptive Set Theory written by Alexander Kechris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.