The Hardy space of a slit domain

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書誌事項

The Hardy space of a slit domain

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

(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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詳細情報

  • NII書誌ID(NCID)
    BA91283706
  • ISBN
    • 9783034600972
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Basel
  • ページ数/冊数
    xix, 124 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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