Invariant Subspaces of the Harmonic Dirichlet Space with Large Co-Dimension
نویسندگان
چکیده
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 0 < α < 1.
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