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 Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 989–1020 (Mi izv1917)

The moment problem, interpolation and basicity

Yu. F. Korobeinik

Abstract: The article contains criteria for the solvability of the general moment problem in countably Hilbert spaces. The relationship between the general interpolation problem in reflexive spaces and the corresponding moment problem is also established. The results lead on the one hand to criteria for solvability of the general interpolation problem (and, in particular, of the Hermite problem) in various function spaces, and, on the other hand, to necessary and sufficient conditions for a system $ż^{p_k}f(\lambda_kz)\}$, where $f$ is an entire function, to form a basis in its linear hull.
Bibliography: 27 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 277–306

Bibliographic databases:

UDC: 517.52+513.88
MSC: 30E05, 30B60

Citation: Yu. F. Korobeinik, “The moment problem, interpolation and basicity”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 989–1020; Math. USSR-Izv., 13:2 (1979), 277–306

Citation in format AMSBIB
\Bibitem{Kor78} \by Yu.~F.~Korobeinik \paper The moment problem, interpolation and basicity \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1978 \vol 42 \issue 5 \pages 989--1020 \mathnet{http://mi.mathnet.ru/izv1917} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=513911} \zmath{https://zbmath.org/?q=an:0405.46030} \transl \jour Math. USSR-Izv. \yr 1979 \vol 13 \issue 2 \pages 277--306 \crossref{https://doi.org/10.1070/IM1979v013n02ABEH002044} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800005} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. W. Krabs, “Optimal control of processes governed by partial differential equations part II: Vibrations”, Zeitschrift für Operations Research, 26:1 (1982), 63
2. A. V. Bratishchev, “A type of lower estimate for entire functions of finite order, and some applications”, Math. USSR-Izv., 24:3 (1985), 415–438
3. Rodney Nillsen, “Functions with piecewise linear Fourier transforms”, Journal of Mathematical Analysis and Applications, 157:2 (1991), 301
4. W. Krabs, G. Leugering, “On boundary controllability of one-dimensional vibrating systems byW01,p-controls forp ∈ [2, ∞]”, Math Meth Appl Sci, 17:2 (1994), 77
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