General elementary solution of a $q$-sided convolution type homogeneous equation
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Yu. S. Saranchuk and A. B. Shishkin;
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 34 (2023), 695-713
- DOI: https://doi.org/10.1090/spmj/1774
- Published electronically: July 26, 2023
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Abstract:
Exponential polynomials satisfying a homogeneous equation of convolution type are called its elementary solutions. The article is devoted to convolution-type operators in the complex domain that generalize the well-known operators of $q$-sided convolution and $\pi$-convolution. The properties of such operators are investigated and the general form of elementary solutions (general elementary solution) of a homogeneous equation of $q$-sided convolution type is described.References
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Bibliographic Information
- Yu. S. Saranchuk
- Affiliation: Kuban′ State University, ul. Stavrapolskaya, 149, 350040, Krasnodar, Russia
- Email: 89182859942@mail.ru
- A. B. Shishkin
- Affiliation: Kuban′ State University, ul. Stavrapolskaya, 149, 350040, Krasnodar, Russia
- Email: shishkin-home@mail.ru
- Received by editor(s): December 25, 2021
- Published electronically: July 26, 2023
- © Copyright 2023 American Mathematical Society
- Journal: St. Petersburg Math. J. 34 (2023), 695-713
- MSC (2020): Primary 30D20
- DOI: https://doi.org/10.1090/spmj/1774