Abstract
In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f -* (f) 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 C D with dim(.F/(F) = n, n E N U foo}. We will also generalize this to the Dirichlet classes D,, 0 < a < 0o, as well as the Besov classes Bp, 1 < p < 00, 0 < a < 1.
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