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

This article is cited in 6 scientific papers (total in 6 papers)

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.

Full text: PDF file (457 kB)
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UDC: 517.5
Received: 05.06.2011

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
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    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. O. A. Krivosheyeva, “Convergence domain for series of exponential polynomials”, Ufa Math. J., 5:4 (2013), 82–87  mathnet  crossref  elib
    3. A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316  mathnet  crossref  mathscinet  isi  elib
    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  mathnet  crossref  mathscinet  isi  elib
    5. O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufa Math. J., 9:3 (2017), 100–108  mathnet  crossref  isi  elib
    6. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77  mathnet  crossref  isi
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