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

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Copyright © 1996 American Mathematical Society. This article first appeared in Proceedings of the American Mathematical Society 124:6 (1996), 1841-1846.

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