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Author : Hiroyuki Takagi
Publisher :
Page : 214 pages
File Size : 34,93 MB
Release : 1992
Category :
ISBN :
Author : R.K. Singh
Publisher : Elsevier
Page : 327 pages
File Size : 19,20 MB
Release : 1993-11-03
Category : Mathematics
ISBN : 0080872905
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.
Page : 266 pages
File Size : 35,24 MB
Release : 1998
Category : Mathematics
ISBN : 0821807684
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 : Carl C. Cowen Jr.
Publisher : Routledge
Page : 404 pages
File Size : 24,32 MB
Release : 2019-03-04
Category : Mathematics
ISBN : 1351459139
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
Page : 401 pages
File Size : 13,91 MB
Release : 2019-03-04
Category : Mathematics
ISBN : 1351459147
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
Page : 229 pages
File Size : 28,9 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461208874
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 : 盧靜安
Publisher : Open Dissertation Press
Page : 54 pages
File Size : 49,42 MB
Release : 2017-01-27
Category : Mathematics
ISBN : 9781374729827
This dissertation, "Weighted Composition Operators Between Lp-spaces" by 盧靜安, Ching-on, Lo, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled WEIGHTED COMPOSITION OPERATORS BETWEEN L -SPACES submitted by LO Ching-on for the degree of Master of Philosophy at The University of Hong Kong in October 2002 Let (X,Σ,μ) and (Y,Γ,ν) be two σ-finite and complete measure spaces. For a Γ-measurable function u: Y → C and a non-singular measurable transformation ϕ Y → X, a linear map uC from L (μ) (1 consisting of (equivalence classes of) Γ-measurable functions on Y was defined by uC (f)(y): =u(y)f(ϕ(y)) for any f ∈L (μ) and y∈Y. Thismapisknownasaweightedcompositionoperator. Wewereinterestedinprop- erties of such class of operators between L -spaces. Weighted composition operators appear in various contexts in the literature. However, there are relatively few results about these operators from L (μ) into L (ν), when p and q are distinct. The boundedness, closedness of ranges and com- pactness of these operators for 1 When the L -spaces are weighted sequence spaces, the invertibility of uC and ϕ arerelatedanditwasprovedthattheinverseofuC isaweightedcompositionmap. The case that either p = ∞ or q = ∞ was considered. In particular, it was shown that when (X,Σ,μ) is non-atomic, the only compact weighted composition map between L -spaces is the zero operator. The spectrum of a compact weighted composition operator on L (μ) was also determined. DOI: 10.5353/th_b3014774 Subjects: Composition operators Lp spaces
Author : Paul Bourdon
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 33,79 MB
Release : 1997
Category : Mathematics
ISBN : 0821806300
We undertake a systematic study of cyclic phenomena for composition operators. Our work shows that composition operators exhibit strikingly diverse types of cyclic behavior, and it connects this behavior with classical problems involving complex polynomial approximation and analytic functional equations.
Author : W. Rudin
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 24,90 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461380987
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.
Author : Frédéric Bayart
Publisher : Cambridge University Press
Page : 352 pages
File Size : 10,93 MB
Release : 2009-06-04
Category : Mathematics
ISBN : 0521514967
The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.