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A criterion for the fundamental principle to hold for invariant subspaces on bounded convex domains in the complex plane. (English. Russian original) Zbl 1274.46063
Funct. Anal. Appl. 46, No. 4, 249-261 (2012); translation from Funkts. Anal. Prilozh. 46, No. 4, 14-30 (2012).
Summary: 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.

46E15 Banach spaces of continuous, differentiable or analytic functions
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