Overview
- Authors:
-
-
Alexandru Aleman
-
Centre for Mathematical Sciences, Lund University, Lund, Sweden
-
William T. Ross
-
Department of Mathematics and Computer Science, University of Richmond, Richmond, USA
-
Nathan S. Feldman
-
Department of Mathematics, Washington & Lee University, Lexington, USA
- Only book which covers Hardy spaces of slit domains
- Includes supplementary material: sn.pub/extras
Access this book
Other ways to access
Table of contents (11 chapters)
-
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 1-7
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 9-23
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 25-46
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 47-57
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 59-63
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 65-77
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 79-83
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 85-91
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 93-96
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 97-112
-
- Alexandru Aleman, William T. Ross, Nathan S. Feldman
Pages 113-114
-
Back Matter
Pages 115-124
About this book
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 .
Reviews
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)
Authors and Affiliations
-
Centre for Mathematical Sciences, Lund University, Lund, Sweden
Alexandru Aleman
-
Department of Mathematics and Computer Science, University of Richmond, Richmond, USA
William T. Ross
-
Department of Mathematics, Washington & Lee University, Lexington, USA
Nathan S. Feldman
