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Σary, Moorhead State University, Mathematics Department
Σary, Moorhead State University, Mathematics Department
Math Department Newsletters
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Invariant Subspaces Of The Harmonic Dirichlet Space With Large Co-Dimension, William T. Ross
Invariant Subspaces Of The Harmonic Dirichlet Space With Large Co-Dimension, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F/ζF) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 <α< ∞, as well as the Besov classes Bα p , 1