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Algebra i Analiz, 2010, Volume 22, Issue 5, Pages 49–68 (Mi aa1204)  

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

Research Papers

Entire functions of sine type and their applications

R. A. Bashmakova, A. A. Putintsevaa, R. C. Yulmukhametovb

a Bashkir State University, Ufa, Russia
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: For subharmonic functions that depend only on the real part of $z$, new constructions of “sine type functions” are presented. This term is reserved for entire functions whose deviation from a given function is majorized, everywhere except some collection of disks, by a certain constant. It is shown that the system of exponentials constructed by the zeros of a sine type function for some convex function is complete and minimal in a certain weighted Hilbert space on an interval of the real line.

Keywords: entire functions, Hilbert spaces, completeness and minimality for a system of exponentials, Fourier–Laplace transformation.

Full text: PDF file (276 kB)
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English version:
St. Petersburg Mathematical Journal, 2011, 22:5, 737–750

Bibliographic databases:

Received: 17.07.2009

Citation: R. A. Bashmakov, A. A. Putintseva, R. C. Yulmukhametov, “Entire functions of sine type and their applications”, Algebra i Analiz, 22:5 (2010), 49–68; St. Petersburg Math. J., 22:5 (2011), 737–750

Citation in format AMSBIB
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\by R.~A.~Bashmakov, A.~A.~Putintseva, R.~C.~Yulmukhametov
\paper Entire functions of sine type and their applications
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 5
\pages 49--68
\mathnet{http://mi.mathnet.ru/aa1204}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2828826}
\zmath{https://zbmath.org/?q=an:1244.30045}
\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 5
\pages 737--750
\crossref{https://doi.org/10.1090/S1061-0022-2011-01165-3}
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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. V. I. Lutsenko, R. S. Yulmukhametov, “O tochnosti asimptoticheskoi approksimatsii subgarmonicheskikh funktsii logarifmom modulya tseloi funktsii”, Ufimsk. matem. zhurn., 2:3 (2010), 46–53  mathnet  zmath  elib
    2. K. P. Isaev, K. V. Trunov, “Raspredelenie pokazatelei bezuslovnogo bazisa iz eksponent v prostranstvakh so stepennym vesom”, Ufimsk. matem. zhurn., 4:1 (2012), 63–70  mathnet
    3. K. P. Isaev, R. S. Yulmukhametov, A. A. Yunusov, “Entire functions with fine asymptotic estimates for convex functions”, Ufa Math. J., 6:2 (2014), 35–43  mathnet  crossref  elib
    4. R. A. Bashmakov, A. A. Makhota, K. V. Trounov, “On absence conditions of unconditional bases of exponents”, Ufa Math. J., 7:2 (2015), 17–32  mathnet  crossref  isi  elib
    5. A. A. Yunusov, “On unconditional exponential bases in weighted spaces on real axis”, Ufa Math. J., 7:3 (2015), 108–118  mathnet  crossref  isi  elib
    6. K. P. Isaev, R. S. Yulmukhametov, A. A. Yunusov, “On unconditional exponential bases in weighted spaces on interval of real axis”, St. Petersburg Math. J., 28:5 (2017), 689–706  mathnet  crossref  mathscinet  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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