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Probl. Anal. Issues Anal., 2018, Volume 7(25), special issue, Pages 137–152 (Mi pa238)  

Elementary solutions of a homogeneous $q$-sided convolution equation

A. A. Tatarkin, U. S. Saranchuk

Kuban State University, 149 Stavropolskaya st., Krasnodar 350040, Russia

Abstract: Spectral synthesis on the complex plane related to solutions of some homogeneous equations of convolution type. There is a method to obtain solutions: we describe the elementary solutions set of the equation (spectral analysis) and prove the approximation theorem (spectral synthesis). In this paper we use the method for some homogeneous equations of convolution type, which appears from spectral synthesis problem for some differential operator.

Keywords: differential operator, holomorphic function, spectral synthesis, spectral analysis, shift operator, convolution equation.

DOI: https://doi.org/10.15393/j3.art.2018.5410

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Bibliographic databases:

UDC: 517.53/.55
MSC: 34L05
Received: 21.05.2018
Revised: 03.09.2018
Accepted:03.09.2018
Language:

Citation: A. A. Tatarkin, U. S. Saranchuk, “Elementary solutions of a homogeneous $q$-sided convolution equation”, Probl. Anal. Issues Anal., 7(25), special issue (2018), 137–152

Citation in format AMSBIB
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\by A.~A.~Tatarkin, U.~S.~Saranchuk
\paper Elementary solutions of a homogeneous $q$-sided convolution equation
\jour Probl. Anal. Issues Anal.
\yr 2018
\vol 7(25)
\pages 137--152
\issueinfo special issue
\mathnet{http://mi.mathnet.ru/pa238}
\crossref{https://doi.org/10.15393/j3.art.2018.5410}
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\elib{https://elibrary.ru/item.asp?id=35688769}


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