Interpolation by Series of Exponential Functions Whose Exponents Are Condensed in a Certain Direction

被引：0

作者：

Merzlyakov S.G. ^{[1
]}

Popenov S.V. ^{[1
]}

机构：

[1] Institute of Mathematics with Computing Center, Ufa Federal Research Center of the Russian Academy of Sciences, Ufa

来源：

Journal of Mathematical Sciences | 2021年 / 257卷 / 3期

关键词：

30D05; 30E05; Cauchy problem; convolution operator; exponent of exponential function; interpolation; limit direction of exponents; Radon integral; series of exponential functions; Vallée Poussin problem;

D O I：

10.1007/s10958-021-05487-z

中图分类号：

学科分类号：

摘要：

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. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：334 / 352

页数：18

共 27 条

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