The Hardy Space of a Slit Domain (Paperback, 2009 ed.)

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 .

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Frontiers in Mathematics
Release date:	August 2009
First published:	2009
Authors:	Alexandru Aleman • Nathan S. Feldman • William T Ross
Dimensions:	240 x 170 x 8mm (L x W x T)
Format:	Paperback
Pages:	144
Edition:	2009 ed.
ISBN-13:	978-3-03-460097-2
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
LSN:	3-03-460097-6
Barcode:	9783034600972

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