Geodesic
A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 14-30

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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.
Keywords: analytic function, invariant subspace, fundamental principle.
Mots-clés : convex domain 
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     author = {O. A. Krivosheeva and A. S. Krivosheev},
     title = {A {Criterion} for the {Fundamental} {Principle} to {Hold} for {Invariant} {Subspaces} on {Bounded} {Convex} {Domains} in the {Complex} {Plane}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {46},
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O. A. Krivosheeva; A. S. Krivosheev. A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 14-30. http://geodesic.mathdoc.fr/item/FAA_2012_46_4_a1/