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Sbornik: Mathematics, 2004, Volume 195, Issue 1, Pages 135–148
DOI: https://doi.org/10.1070/SM2004v195n01ABEH000797
(Mi sm797)
 

This article is cited in 2 scientific papers (total in 2 papers)

An approximation theorem for entire functions of exponential type and stability of zero sequences

B. N. Khabibullin

Bashkir State University
References:
Abstract: Let L be an entire function of exponential type in C with indicator function hL; let Λ={λn}, n=1,2,, be a subsequence of zeros of the entire function of exponential type L0; let Γ={γn} be a complex number sequence and assume that
n|1λn1γn|<.

A simple construction of a sequence of entire functions of exponential type {Ln} transforming Λ into a subsequence Γ of zeros of an entire function of exponential type G0 such that hG=hL is put forward (an approximation theorem). This result is applied to stability problems of zero sequences and non-uniqueness sequences for spaces of entire functions of exponential type with constraints on the indicators and to the problem of the stability of the completeness property of exponential systems in the space of germs of analytic functions on a compact convex set.
Received: 30.08.2001 and 12.05.2003
Bibliographic databases:
UDC: 517.547.22+517.982.274+517.538.2
MSC: 30D20, 30D15
Language: English
Original paper language: Russian
Citation: B. N. Khabibullin, “An approximation theorem for entire functions of exponential type and stability of zero sequences”, Sb. Math., 195:1 (2004), 135–148
Citation in format AMSBIB
\Bibitem{Kha04}
\by B.~N.~Khabibullin
\paper An approximation theorem for entire functions of
exponential type and stability of zero sequences
\jour Sb. Math.
\yr 2004
\vol 195
\issue 1
\pages 135--148
\mathnet{http://mi.mathnet.ru/eng/sm797}
\crossref{https://doi.org/10.1070/SM2004v195n01ABEH000797}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2058381}
\zmath{https://zbmath.org/?q=an:1065.30025}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000221431900008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-2542571795}
Linking options:
  • https://www.mathnet.ru/eng/sm797
  • https://doi.org/10.1070/SM2004v195n01ABEH000797
  • https://www.mathnet.ru/eng/sm/v195/i1/p143
  • This publication is cited in the following 2 articles:
    1. E. G. Kudasheva, B. N. Khabibullin, “Variation of subharmonic function under transformation of its Riesz measure”, Zhurn. matem. fiz., anal., geom., 3:1 (2007), 61–94  mathnet  mathscinet  zmath  elib
    2. B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:629
    Russian version PDF:249
    English version PDF:17
    References:79
    First page:1
     
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