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Matematicheskie Zametki, 2021, Volume 109, Issue 3, Pages 380–396
DOI: https://doi.org/10.4213/mzm12678 (Mi mzm12678) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Invariant Spaces of Entire Functions

A. S. Krivosheeva, O. A. Krivosheevab

a Institute of Mathematics with Computing Centre, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa
b Bashkir State University, Ufa
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DOI: https://doi.org/10.4213/mzm12678
Abstract: Subspaces of the space of analytic functions on a convex domain in the complex plane that are invariant with respect to the differentiation operator are studied. The problem of continuing all functions in an invariant subspace to entire functions is investigated. A simple geometric criterion for the existence of such a continuation is obtained. A criterion for the functions from an invariant subspace to be represented by a series of exponential monomials is also obtained. These monomials are the eigenfunctions and generalized eigenfunctions of the differentiation operator on the invariant subspace.
Keywords: invariant subspace, analytic continuation, exponential monomial, entire function, series of exponentials.
Funding agency Grant number
Contest «Young Russian Mathematics»
The work of O. A. Krivosheeva was supported in part by the “Young Russian Mathematics” award.
Received: 18.01.2020
Revised: 10.11.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 3, Pages 413–426
DOI: https://doi.org/10.1134/S0001434621030093
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. S. Krivosheev, O. A. Krivosheeva, “Invariant Spaces of Entire Functions”, Mat. Zametki, 109:3 (2021), 380–396; Math. Notes, 109:3 (2021), 413–426
Citation in format AMSBIB
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\paper Invariant Spaces of Entire Functions
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\pages 380--396
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\transl
\jour Math. Notes
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\vol 109
\issue 3
\pages 413--426
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    • This publication is cited in the following 1 articles:
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