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 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 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 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 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 Unbounded Weighted Composition Operators in L2 Spaces written by Piotr Budzyński and published by Springer. This book was released on 2018-05-28 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized. The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types. The book is primarily aimed at researchers in single or multivariable operator theory.
Download or read book Cyclic Phenomena for Composition Operators written by Paul Bourdon and published by American Mathematical Soc.. This book was released on 1997 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Composition Operators on Hardy Orlicz Spaces written by Pascal Lefèvre and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Psi grows rapidly: compactness, weak compactness, to be p-summing, order bounded, ... , and show how these notions behave according to the growth of Psi. They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces."--Publisher's description.
Download or read book Concrete Operators Spectral Theory Operators in Harmonic Analysis and Approximation written by Manuel Cepedello Boiso and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.
Download or read book Operator Algebras Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.
Download or read book Algebra Geometry Analysis and their Applications written by Naseem Ahmad and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2016-11-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles appeared in this book have been contributed by well-known mathematician and scientists projecting the modern development in the subject. This book covers the following topics Geometry Algebra Functional Analysis Fuzzy Topology Complex Analysis TribologyPostgraduates and researchers working in the areas of mathematics and mathematical sciences will find this book to be of immense value.
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 Handbook of Analytic Operator Theory written by Kehe Zhu and published by CRC Press. This book was released on 2019-05-10 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references. The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before. Features: The editor of the handbook is a widely known and published researcher on this topic The handbook's contributors are a who's=who of top researchers in the area The first contributed volume on these diverse topics
Download or read book Topics in Complex Analysis and Operator Theory written by Oscar Blasco and published by American Mathematical Soc.. This book was released on 2012 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.
Download or read book Recent Advances in Operator Theory Operator Algebras and their Applications written by Dumitru Gaspar and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Download or read book Problems and Recent Methods in Operator Theory written by Fernanda Botelho and published by American Mathematical Soc.. This book was released on 2017-04-18 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Geometry Algebra and Analysis written by Mohammad Hasan Shahid and published by Springer Nature. This book was released on 2020-09-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of selected research papers, some of which were presented at the International Conference on Differential Geometry, Algebra and Analysis (ICDGAA 2016), held at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 15–17 November 2016. It covers a wide range of topics—geometry of submanifolds, geometry of statistical submanifolds, ring theory, module theory, optimization theory, and approximation theory—which exhibit new ideas and methodologies for current research in differential geometry, algebra and analysis. Providing new results with rigorous proofs, this book is, therefore, of much interest to readers who wish to learn new techniques in these areas of mathematics.
