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

S. G. Merzlyakov ; S. V. Popenov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 62-79.

Résumé

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.

Détail

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

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