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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 88–106 (Mi ufa136)

An almost exponential sequence of exponential polynomials

A. S. Krivosheyev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: A special sequence of exponential polynomials, whose exponentials are divided into relatively small groups, is studied in the article. It is proved that this sequence is almost an exponential sequence for each convex domain of a complex plane. By means of this result necessary and sufficient conditions for the considered sequence to be a basis in a closed and invariant under differentiation subspace of the space of analytic functions in a convex domain are obtained. Two methods of description of the whole class of bases in an invariant subspace, whose elements are exponential polynomials, are given.

Keywords: exponential polynomial, invariant subspace, analytic function, convex domain, basis.

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Citation: A. S. Krivosheyev, “An almost exponential sequence of exponential polynomials”, Ufimsk. Mat. Zh., 4:1 (2012), 88–106

Citation in format AMSBIB
\Bibitem{Kri12} \by A.~S.~Krivosheyev \paper An almost exponential sequence of exponential polynomials \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 1 \pages 88--106 \mathnet{http://mi.mathnet.ru/ufa136} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. S. Krivosheev, O. A. Krivosheeva, “A basis in an invariant subspace of analytic functions”, Sb. Math., 204:12 (2013), 1745–1796
2. O. A. Krivosheyeva, “Convergence domain for series of exponential polynomials”, Ufa Math. J., 5:4 (2013), 82–87
3. A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316
4. O. A. Krivosheyeva, A. S. Krivosheyev, “A representation of functions from an invariant subspace with almost real spectrum”, St. Petersburg Math. J., 29:4 (2018), 603–641
5. O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufa Math. J., 9:3 (2017), 100–108
6. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77
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