The Hardy Space of a Slit Domain by Alexandru AlemanThe Hardy Space of a Slit Domain by Alexandru Aleman

The Hardy Space of a Slit Domain

byAlexandru Aleman, Nathan S. Feldman, William T. Ross

Paperback | August 14, 2009

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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 .
Title:The Hardy Space of a Slit DomainFormat:PaperbackDimensions:144 pagesPublished:August 14, 2009Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034600976

ISBN - 13:9783034600972


Table of Contents

Preface; Notation; List of Symbols; Preamble; 1 Introduction; 2 Preliminaries; 3 Nearly invariant subspaces; 4 Nearly invariant and the backward shift; 5 Nearly invariant and de Branges spaces; 6 Invariant subspaces of the slit disk; 7 Cyclic invariant subspaces; 8 The essential spectrum; 9 Other applications; 10 Domains with several slits; 11 Final thoughts; 12 Appendix

Editorial Reviews

From the reviews:"This memoir is concerned with the description of the shift-invariant subspaces of a Hardy space on a slit domain . . this brief monograph represents an interesting and valuable contribution to the literature on the subject of shift-invariant subspaces. It should be helpful for researchers and advanced graduate students specializing in the field." (Dragan Vukotic, Mathematical Reviews, Issue 2011 m)