A criterion for the fundamental principle to hold for invariant subspaces on bounded convex domains in the complex plane |
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Authors: | O A Krivosheeva A S Krivosheev |
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Institution: | 1. Bashkir State University, Ufa, Russia 2. Institute for Mathematics and Computer Center, Ural Scientific Center, Russian Academy of Sciences, Sverdlovsk, Russia
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Abstract: | Let D be a bounded convex domain of the complex plane. We study the problem of whether the fundamental principle holds for analytic function spaces on D invariant with respect to the differentiation operator and admitting spectral synthesis. Earlier this problem was solved under a restriction on the multiplicities of the eigenvalues of the differentiation operator. In the present paper, we lift this restriction. Thus, we present a complete solution of the fundamental principle problem for arbitrary nontrivial closed invariant subspaces admitting spectral synthesis on arbitrary bounded convex domains. |
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