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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 162, Pages 62–79 (Mi into442)

Interpolation by series of exponential functions whose exponents are condensed in a certain direction

S. G. Merzlyakov, S. V. Popenov

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

Abstract: For complex interpolation nodes, we study the problem of interpolation by series of exponential functions whose exponents form a set, which is condensed at infinity in a certain direction. We obtain a criterion for all sets of nodes from a special class. For arbitrary sets of nodes, we obtain a necessary condition for the solvability of a more general problem of interpolation by functions that can be represented as Radon integrals of an exponential function over a set of exponents. The paper also contains well-known results on interpolation, which, in particular, allow studying the multipoint holomorphic Vallée Poussin problem for convolution operators.

Keywords: series of exponential functions, exponent of exponential function, limit direction of exponents, interpolation, convolution operator, Cauchy problem, Vallée Poussin problem, Radon integral

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Bibliographic databases:
UDC: 517.98
MSC: 30E05, 30D05

Citation: S. G. Merzlyakov, S. V. Popenov, “Interpolation by series of exponential functions whose exponents are condensed in a certain direction”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 62–79

Citation in format AMSBIB
\Bibitem{MerPop19} \by S.~G.~Merzlyakov, S.~V.~Popenov \paper Interpolation by series of exponential functions whose exponents are condensed in a certain direction \inbook Complex Analysis. Mathematical Physics \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2019 \vol 162 \pages 62--79 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into442} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3981818}