[PDF] Compact Composition Operators On Weighted Hardy And Bergman Spaces eBook

Author : Elhadi Dalam
Publisher : LAP Lambert Academic Publishing
Page : 164 pages
File Size : 33,79 MB
Release : 2012
Category : Bergman spaces
ISBN : 9783846527412

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Over the last ten years, the theory of Hardy and Bergman Spaces has undergone a remarkable metamorphosis. The research originated from a study of weighted Hardy and Bergman Spaces that revolve around the composition operators and inequalities is to present the latest development, mostly achieved in the thesis form. In particular, gradute students and new researchers in the field will have access to the theory from an almost self contained and readable source. We study the action of composition operators on Sobolev Spaces of analytic functions in some weighted Bergman and Hardy Spaces on the unit disc. composition operators mapping into the Hardy Space are included by making particular choices for the weights. In the thesis we will explain some of the important results of compact composition operators on weighted Hardy and Bergman Spaces.

Author : Rocky Mountain Mathematics Consortium
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 50,70 MB
Release : 1998
Category : Mathematics
ISBN : 0821807684

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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 : 401 pages
File Size : 17,47 MB
Release : 2019-03-04
Category : Mathematics
ISBN : 1351459147

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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 : Jose Angel Pelaez
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 28,11 MB
Release : 2014-01-08
Category : Mathematics
ISBN : 0821888021

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This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.

Author : Joel H. Shapiro
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 20,58 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461208874

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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 : Pascal Lefèvre
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 11,28 MB
Release : 2010
Category : Mathematics
ISBN : 082184637X

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"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.

Author : Christopher Hammond
Publisher :
Page : 272 pages
File Size : 13,59 MB
Release : 2010
Category : Composition operators
ISBN :

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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.