Functional Analysis and Its Applications

, Volume 46, Issue 4, pp 249–261 | Cite as

A criterion for the fundamental principle to hold for invariant subspaces on bounded convex domains in the complex plane

  • O. A. Krivosheeva
  • A. S. Krivosheev


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.

Key words

analytic function convex domain invariant subspace fundamental principle 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Bashkir State UniversityUfaRussia
  2. 2.Institute for Mathematics and Computer Center, Ural Scientific CenterRussian Academy of SciencesSverdlovskRussia

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