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Mat. Sb. (N.S.), 1986, Volume 131(173), Number 3(11), Pages 309–322 (Mi msb1926)  

This article is cited in 4 scientific papers (total in 5 papers)

On absolute completeness of systems of exponentials on a closed interval

I. F. Krasichkov-Ternovskii


Abstract: Let $\Lambda=\{\lambda_i\}$ be a sequence of points in the complex plane, and $M=\{m_i\}$ a sequence of positive numbers. Problem: under what relations between $\Lambda$ and $M$ can any function in $C[a,b]$ be approximated in the uniform norm by finite linear combinations $\sum a_ie^{\lambda_ix}$ of exponentials with the coefficient restriction $|a_i|\leqslant C_fm_i$. Here $C_f$ depends only on $f$.
An exact solution of the problem is given under the assumption that $|\frac{\operatorname{Im}\lambda_i}{\operatorname{Re}\lambda_i}|\leqslantConst$.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 59:2, 303–315

Bibliographic databases:

UDC: 517.5
MSC: Primary 30B50, 30B60, 41A30; Secondary 30D15
Received: 18.03.1985

Citation: I. F. Krasichkov-Ternovskii, “On absolute completeness of systems of exponentials on a closed interval”, Mat. Sb. (N.S.), 131(173):3(11) (1986), 309–322; Math. USSR-Sb., 59:2 (1988), 303–315

Citation in format AMSBIB
\Bibitem{Kra86}
\by I.~F.~Krasichkov-Ternovskii
\paper On absolute completeness of systems of exponentials on a~closed interval
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 131(173)
\issue 3(11)
\pages 309--322
\mathnet{http://mi.mathnet.ru/msb1926}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=881916}
\zmath{https://zbmath.org/?q=an:0626.42017|0652.42015}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 59
\issue 2
\pages 303--315
\crossref{https://doi.org/10.1070/SM1988v059n02ABEH003137}


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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. B. N. Khabibullin, “Sets of uniqueness in spaces of entire functions of a single variable”, Math. USSR-Izv., 39:2 (1992), 1063–1084  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. B. N. Khabibullin, “A uniqueness theorem for subharmonic functions of finite order”, Math. USSR-Sb., 73:1 (1992), 195–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. I. F. Krasichkov-Ternovskii, G. N. Shilova, “Absolute completeness of systems of exponentials on convex compact sets”, Sb. Math., 196:12 (2005), 1801–1814  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. B. Sherstyukov, “Dual characterization of absolutely representing systems in inductive limits of Banach spaces”, Siberian Math. J., 51:4 (2010), 745–754  mathnet  crossref  mathscinet  isi  elib  elib
    5. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192  mathnet
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