Download or read book On the Norm of a Composition Operator written by Christopher Nathan Brodsky Hammond and published by . This book was released on 2003 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Composition Operators written by Joel H. Shapiro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Composition Operators on Function Spaces written by R.K. Singh and published by Elsevier. This book was released on 1993-11-03 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Download or read book Norm Inequalities for Composition Operators on Hardy and Weighted Bergman Spaces written by Christopher Hammond and published by . This book was released on 2010 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Any analytic self-map of the open unit disk induces a bounded composition operator on the Hardy space H 2 and on the standard weighted Bergman spaces A 2 [beta symbol]. For a particular self-map, it is reasonable to wonder whether there is any meaningful relationship between the norms of the corresponding operators acting on each of these spaces. In this paper, we demonstrate an inequality which, at least to a certain degree, provides an answer to this question.

Download or read book Topological Structure and Banach Ideals of Composition Operators written by Thomas E. Goebeler and published by . This book was released on 1999 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Composition Operators on Spaces of Analytic Functions written by Carl C. Cowen Jr. and published by Routledge. This book was released on 2019-03-04 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Studies on Composition Operators written by Rocky Mountain Mathematics Consortium and published by American Mathematical Soc.. This book was released on 1998 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Essential Norm and Spectrum of Composition Operators on Space of Bounded Analytic Functions written by Lixin Zheng and published by . This book was released on 2000 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Norm and Essential Norm Estimates of Composition Operators on Besov Type Spaces written by Robert Lee Donaway and published by . This book was released on 1999 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Operator Theory written by Joseph A. Ball and published by Springer Science & Business Media. This book was released on 2011-02-09 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Download or read book Composition Operators on Spaces of Analytic Functions written by Carl C. Cowen, Jr. and published by Routledge. This book was released on 2019-03-04 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Sequences and Series in Banach Spaces written by J. Diestel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.

Download or read book Norms of Composition Operators and Composition Operators Acting as Isometries on the Chebyshev Space written by Ashley L. Potter and published by . This book was released on 2008 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Complex Analysis and Dynamical Systems written by Mark Agranovsky and published by Birkhäuser. This book was released on 2018-01-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

Download or read book Topological Structures on Sets of Composition Operators written by Carl Toews and published by . This book was released on 2002 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Studies on Composition Operators and Function Spaces written by Marko Kotilainen and published by . This book was released on 2007 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.