The Hardy Space of a Slit Domain

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Aleman, Alexandru (Autor), Feldman, Nathan S. (Autor), Ross, William T. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2009.
Edición:1st ed. 2009.
Colección:Frontiers in Mathematics,
Temas:
Functions of complex variables.
Functions of a Complex Variable.
Acceso en línea:Texto Completo

MARC

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100 1 |a Aleman, Alexandru.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Hardy Space of a Slit Domain  |h [electronic resource] /  |c by Alexandru Aleman, Nathan S. Feldman, William T. Ross. 
250 |a 1st ed. 2009. 
264 1 |a Basel :  |b Birkhäuser Basel :  |b Imprint: Birkhäuser,  |c 2009. 
300 |a 144 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Frontiers in Mathematics,  |x 1660-8054 
505 0 |a 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. 
520 |a 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 . 
650 0 |a Functions of complex variables. 
650 1 4 |a Functions of a Complex Variable. 
700 1 |a Feldman, Nathan S.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Ross, William T.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783034600996 
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830 0 |a Frontiers in Mathematics,  |x 1660-8054 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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