Interpolation by sums of series of exponentials and global Cauchy problem for convolution operators
- Authors: Merzlyakov S.G.1, Popenov S.V.1
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Affiliations:
- Ufa Branch of the Russian Academy of Sciences
- Issue: Vol 485, No 2 (2019)
- Pages: 149-152
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12826
- DOI: https://doi.org/10.31857/S0869-56524852149-152
- ID: 12826
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Abstract
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are obtained that give solubility of the problem. A new approach is demonstrated that enable us, for the case of holomorphic function in a domain, to obtain criteria of solubility of the problem for some class of exponents set and for a special class of nodes set. Moreover the necessity of the conditions is proved in great generality namely for arbitrary nodes sets and in the setting of interpolation by functions that are represented as the Laplace transforms of the Radon measures over the exponents set. Solubility is obtained of the global Cauchy problem for convolution operator with data on the nodes set in domain, in the form of the series of exponentials whose exponents belong to a sparse subset of zero set of characteristic function of the operator. The results substantially strengthen the known results on the theme.
About the authors
S. G. Merzlyakov
Ufa Branch of the Russian Academy of Sciences
Author for correspondence.
Email: msg2000@mail.ru
Russian Federation, Ufa
S. V. Popenov
Ufa Branch of the Russian Academy of Sciences
Email: spopenov@gmail.com
Russian Federation, Ufa
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