Download Free The Backward Shift On The Hardy Space Book in PDF and EPUB Free Download. You can read online The Backward Shift On The Hardy Space and write the review.

Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator. This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces H{p}. The characterization of the backward shift invariant subspaces of H{p} for 1
If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. They are careful to cover the various types of continuations, attempting to unify them and suggesting some open questions. The book also addresses the role of such continuations in approximation theory and operator theory. The introductory overview provides a useful look at the history and context of the theory.
This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.
This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.
Text for advanced undergraduate and graduate students introduces Hilbert space and analytic function theory. Its principal feature is the extensive use of formal power series methods to obtain and sometimes reformulate results of analytic function theory. 1966 edition.
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.