Geodesic
A~fundamental principle for invariant subspaces in convex domains
Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 291-353.

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Under certain natural restrictions, we give a complete solution of the interpolation problem in spaces of entire functions of exponential type whose conjugate diagram is contained in a given convex domain. We also give a complete solution of the problem of finding a fundamental principle for arbitrary non-trivial closed subspaces of functions analytic in a convex domain that are invariant under differentiation and admit spectral synthesis. 
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A. S. Krivosheev. A~fundamental principle for invariant subspaces in convex domains. Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 291-353. http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a4/

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