The Hardy space of a slit domain
著者
書誌事項
The Hardy space of a slit domain
(Frontiers in mathematics)
Birkhäuser, 2009
- : pbk.
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注記
Includes bibliographical references and index.
内容説明・目次
内容説明
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 .
目次
- 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
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