TY  - BOOK
AU  - Aleman,Alexandru
AU  - Ross,William T.
AU  - Feldman,Nathan S.
ED  - SpringerLink (Online service)
TI  - The Hardy Space of a Slit Domain
T2  - Frontiers in Mathematics,
SN  - 9783034600989
AV  - QA331-355 
U1  - 515.9 23
PY  - 2009///
CY  - Basel
PB  - Birkhäuser Basel
KW  - Mathematics
KW  - Functions of complex variables
KW  - Functions of a Complex Variable
KW  - Electronic books
KW  - local
N1  - 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
N2  - 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
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/978-3-0346-0098-9
ER  -