Geodesic
A~criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane
Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 43-76.

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We study subspaces invariant under differentiation in spaces of analytic functions in convex domains of the complex plane. For arbitrary convex domains we get a criterion for analytic continuation of functions from arbitrary non-trivial closed invariant subspaces admitting spectral synthesis. 
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A. S. Krivosheev. A~criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane. Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 43-76. http://geodesic.mathdoc.fr/item/IM2_2004_68_1_a2/

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