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arXiv · 1612.05972

Interpolation by sums of the series of exponentials in $H (\mathbb C)$ with interpolation nodes on the rays

S. G. Merzlyakov·S. V. Popenov
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Abstract

In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the problem in the case when all infinite portions of interpolation nodes are situated on a finite system of rays. It is also disclosed that the problem is equivalent to particular problems of simple interpolation, as well as of point-wise crude approximation, by sums of the series of exponentials.

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S. G. Merzlyakov, S. V. Popenov. 2016-12-18. Interpolation by sums of the series of exponentials in $H (\mathbb C)$ with interpolation nodes on the rays. https://arxiv.org/abs/1612.05972

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