Invariant subspaces of the harmonic Dirichlet space with large co-dimension

Author:
William T. Ross

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1841-1846

MSC (1991):
Primary 30H05; Secondary 30C15

DOI:
https://doi.org/10.1090/S0002-9939-96-03243-1

MathSciNet review:
1307561

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift ) of the harmonic Dirichlet space . Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces with , . We will also generalize this to the Dirichlet classes , , as well as the Besov classes , , .

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Additional Information

**William T. Ross**

Affiliation:
Department of Mathematics University of Richmond Richmond, Virginia 23173

Email:
rossb@mathcs.urich.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03243-1

Keywords:
Dirichlet spaces,
invariant subspaces,
co-dimension,
Bergman spaces

Received by editor(s):
October 31, 1994

Received by editor(s) in revised form:
December 9, 1994

Additional Notes:
This research was supported in part by a grant from the National Science Foundation.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society