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This article is cited in 1 scientific paper (total in 1 paper)
Invariant subspaces in unbounded domains
A. S. Krivosheevab, O. A. Krivosheevaba a Baskir State University,
32 Z. Validi St., Ufa 450076, Russia
b Institute of Mathematics,
Ufa Federal Research Center, RAS,
112 Chernyshevsky str., Ufa 450008, Russia
Abstract:
We study subspaces of functions analytic in an unbounded convex domain of the complex plane and invariant with respect to the differentiation operator. This paper is devoted to the study of the problem of representing all functions from an invariant subspace by series of exponential monomials. These exponential monomials are eigenfunctions and associated functions of the differentiation operator in the invariant subspace. A simple geometric criterion of the fundamental principle is obtained. It is formulated just in terms of the Krisvosheev condensation index for the sequence of exponents of the mentioned exponential monomials.
Keywords:
invariant subspace, fundamental principle, exponential monomial, entire function, series of exponents.
Received: 14.06.2021 Revised: 11.09.2021 Accepted: 14.09.2021
Citation:
A. S. Krivosheev, O. A. Krivosheeva, “Invariant subspaces in unbounded domains”, Probl. Anal. Issues Anal., 10(28):3 (2021), 91–107
Linking options:
https://www.mathnet.ru/eng/pa333 https://www.mathnet.ru/eng/pa/v28/i3/p91
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Abstract page: | 70 | Full-text PDF : | 34 | References: | 11 |
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