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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 — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia

Abstract: A theorem due to Eidelheit concerning the interpolation problem for a sequence of continuous linear functionals in a Fréchet space is generalized. A solvability criterion for the interpolation problem is obtained in the form of an absolutely convergent series whose elements are in a fixed set. A solution of the system of equations for a sequence of functionals is constructed explicitly in a particular case. These results are then applied to spaces of holomorphic functions.
Bibliography: 15 titles.

Keywords: Fréchet space, absolutely convergent series, interpolation, continuous linear functionals, spaces of holomorphic functions, series of exponentials.

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

Full text: PDF file (748 kB)
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English version:
Sbornik: Mathematics, 2019, 210:1, 105–144

Bibliographic databases:

Document Type: Article
UDC: 517.982.3+517.53
MSC: Primary 41A05; Secondary 30B50, 46A04, 46E10
Received: 31.12.2016 and 05.07.2018

Citation: S. G. Merzlyakov, “Interpolation and absolutely convergent series in Fréchet spaces”, Mat. Sb., 210:1 (2019), 113–154; Sb. Math., 210:1 (2019), 105–144

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