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The Hardy Space of a Slit Domain: Frontiers in Mathematics

Autor Alexandru Aleman, Nathan S. Feldman, William T. Ross
en Limba Engleză Paperback – 14 aug 2009
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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Specificații

ISBN-13: 9783034600972
ISBN-10: 3034600976
Pagini: 144
Ilustrații: 144 p.
Dimensiuni: 155 x 235 x 8 mm
Greutate: 0.3 kg
Ediția:2009
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Frontiers in Mathematics

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

Preliminaries.- Nearly invariant subspaces.- Nearly invariant and the backward shift.- Nearly invariant and de Branges spaces.- Invariant subspaces of the slit disk.- Cyclic invariant subspaces.- The essential spectrum.- Other applications.- Domains with several slits.- Final thoughts.

Recenzii

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 Vukotić, Mathematical Reviews, Issue 2011 m)

Caracteristici

Only book which covers Hardy spaces of slit domains Includes supplementary material: sn.pub/extras