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＜電子ブック＞
The Hardy Space of a Slit Domain / by Alexandru Aleman, Nathan S. Feldman, William T. Ross
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2009.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2009
本文言語	英語
大きさ	144 p : online resource
著者標目	*Aleman, Alexandru author Feldman, Nathan S author Ross, William T author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables FREE:Functions of a Complex Variable
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0346-0098-9

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