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The Hardy Space of a Slit Domain by Alexandru Aleman

The Hardy Space of a Slit Domain

by Alexandru Aleman
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Book cover type: Paperback
  • ISBN13: 9783034600972
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 144
  • Original Price: EUR 49.99
  • Language: English
  • Edition: 2009
  • Item Weight: 295 grams
  • BISAC Subject(s): Mathematical Analysis, Functional Analysis, and Calculus

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 .

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