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Ufimsk. Mat. Zh., 2010, Volume 2, Issue 1, Pages 97–109 (Mi ufa45)  

This article is cited in 3 scientific papers (total in 3 papers)

Completeness of exponential systems in weighted spaces on real axe

V. V. Napalkova, A. A. Rumyantsevab, R. S. Yulmukhametova

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

Abstract: It is studied the completeness of exponential systems $\exp(\lambda_kt)$ in the Hilbert space $L_2(\mathbb R;a|x|^\alpha)$, where $\alpha\in(1;2]$, $a>0$. We obtain both the necessary and sufficient conditions of completeness in terms of system $\lambda_k$.

Keywords: completeness of exponential systems, Fourier–Laplace transform, convex function, entire function.

Full text: PDF file (450 kB)
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Bibliographic databases:
UDC: 517.54
Received: 15.01.2010

Citation: V. V. Napalkov, A. A. Rumyantseva, R. S. Yulmukhametov, “Completeness of exponential systems in weighted spaces on real axe”, Ufimsk. Mat. Zh., 2:1 (2010), 97–109

Citation in format AMSBIB
\Bibitem{NapRumYul10}
\by V.~V.~Napalkov, A.~A.~Rumyantseva, R.~S.~Yulmukhametov
\paper Completeness of exponential systems in weighted spaces on real axe
\jour Ufimsk. Mat. Zh.
\yr 2010
\vol 2
\issue 1
\pages 97--109
\mathnet{http://mi.mathnet.ru/ufa45}
\zmath{https://zbmath.org/?q=an:1240.30024}


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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. A. Rumyantseva, “Asimptotika $\delta $-subgarmonicheskikh funktsii i ikh assotsiirovannykh mer”, Ufimsk. matem. zhurn., 2:3 (2010), 83–107  mathnet  zmath
    2. A. R. Bagautdinova, A. V. Lutsenko, V. I. Lutsenko, E. D. Shaimuratova, “Integralnye otsenki proizvodnykh analiticheskikh funktsii vne vypuklykh oblastei”, Ufimsk. matem. zhurn., 4:4 (2012), 13–21  mathnet  mathscinet
    3. A. A. Makhota, “On completeness of exponential systems in convex domain”, Ufa Math. J., 10:1 (2018), 76–79  mathnet  crossref  isi  elib
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