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 Mat. Sb., 2019, Volume 210, Number 1, Pages 113–154 (Mi msb8902)

Interpolation and absolutely convergent series in Fréchet spaces

S. G. Merzlyakov

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences

Abstract: The Eidelhelt theorem concerning to an interpolational problem for a sequence of linear continuous functionals in the Frechet space is generalized. The criterion of resolvability of an interpolational problem in the form of a absolutely convergent series which elements lie in the given set is discovered. For one special case constructive construction of a solution of a system of equations for sequence of functionals is obtained.
Further these results are applied to spaces of holomorphic functions.

Keywords: The Frechet space, absolutely convergent series, interpolation, linear continuous functional, space of holomorphic functions, the series of exponentials.

DOI: https://doi.org/10.4213/sm8902

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English version:
DOI: https://doi.org/10.1070/SM8902

Document Type: Article
UDC: 517.982.3+517.53
MSC: 46A04

Citation: S. G. Merzlyakov, “Interpolation and absolutely convergent series in Fréchet spaces”, Mat. Sb., 210:1 (2019), 113–154

Citation in format AMSBIB
\Bibitem{Mer19} \by S.~G.~Merzlyakov \paper Interpolation and absolutely convergent series in Fréchet spaces \jour Mat. Sb. \yr 2019 \vol 210 \issue 1 \pages 113--154 \mathnet{http://mi.mathnet.ru/msb8902} \crossref{https://doi.org/10.4213/sm8902} \elib{http://elibrary.ru/item.asp?id=36603916}