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The fundamental principle for invariant subspaces in convex domains. (English. Russian original) Zbl 1071.30024
Izv. Math. 68, No. 2, 291-353 (2004); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 2, 71-136 (2004).
The author investigates the fundamental principle problem for arbitrary non-trivial closed invariant subspaces of analytic functions in convex domains of the plane that admited spectral synthesis. He has proved the equivalence of this problem and the solubility of the some multiple interpolation problem. For the last one he has obtained the complete solution in the spaces of entire functions of exponential type whose conjugate diagram is contained in a convex domain under some restrictions.

MSC:
30D20 Entire functions of one complex variable, general theory
30D15 Special classes of entire functions of one complex variable and growth estimates
30E05 Moment problems and interpolation problems in the complex plane
46E99 Linear function spaces and their duals
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