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This article is cited in 1 scientific paper (total in 1 paper)
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.
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
Linking options:
https://www.mathnet.ru/eng/sm8902https://doi.org/10.1070/SM8902 https://www.mathnet.ru/eng/sm/v210/i1/p113
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Abstract page: | 523 | Russian version PDF: | 72 | English version PDF: | 24 | References: | 61 | First page: | 34 |
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