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Matematicheskie Zametki, 1974, Volume 15, Issue 2, Pages 213–219 (Mi mzm7338)  

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

The stability of the completeness and minimality in $L^2$ of a system of exponential functions

A. M. Sedletskii

Moscow Power Engineering Institute
Full-text PDF (485 kB) Citations (3)
Abstract: Let the sequences $\{\lambda_n\}$ and $\{\alpha_n\}$ of complex numbers satisfy the conditions: 1) $\sup|\operatorname{Im}\lambda_n|=h<\infty$; 2) the number of points $\lambda_n$ in the rectangle $|t-\operatorname{Re}z|\le1$, $|\operatorname{Im}z|\le h$ is uniformly bounded with respect to $t\in(-\infty,\infty)$; 3) $\{\alpha_n\}\in l^p$ for some $p<\infty$. Then the systems $\{\exp(i\lambda_nx)\}$ and $\{\exp(ix(\lambda_n+\alpha_n))\}$ are simultaneously complete or noncomplete (minimal or nonminimal) in $L^2(-a,a)$ ($a<\infty$).
Received: 05.06.1973
English version:
Mathematical Notes, 1974, Volume 15, Issue 2, Pages 121–124
DOI: https://doi.org/10.1007/BF02102391
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: A. M. Sedletskii, “The stability of the completeness and minimality in $L^2$ of a system of exponential functions”, Mat. Zametki, 15:2 (1974), 213–219; Math. Notes, 15:2 (1974), 121–124
Citation in format AMSBIB
\Bibitem{Sed74}
\by A.~M.~Sedletskii
\paper The stability of the completeness and minimality in $L^2$ of a~system of exponential functions
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 2
\pages 213--219
\mathnet{http://mi.mathnet.ru/mzm7338}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=355472}
\zmath{https://zbmath.org/?q=an:0295.42012}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 2
\pages 121--124
\crossref{https://doi.org/10.1007/BF02102391}
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  • https://www.mathnet.ru/eng/mzm/v15/i2/p213
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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