期刊
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
卷 91, 期 -, 页码 423-438出版社
WILEY
DOI: 10.1112/jlms/jdv001
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资金
- National Science Foundation [DMS-0901642]
The Dirichlet space D is the space of all analytic functions f on the open unit disc D such that f' is square integrable with respect to two-dimensional Lebesgue measure. In this paper, we prove that the invariant subspaces of the Dirichlet shift are in one-to-one correspondence with the kernels of the Dirichlet-Hankel operators. We then apply this result to obtain information about the invariant subspace lattice of the weak product D circle dot D and to some questions about approximation of invariant subspaces of D. Our main results hold in the context of superharmonically weighted Dirichlet spaces.
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