Abstract:
One says that an approximation theorem holds for a homogeneous convolution-type equation if any solution of this equation is approximated by its elementary solutions. In this paper, we state a necessary and sufficient condition for the validity of the approximation theorem for the homogeneous equation of three-way convolution for any choice of a convex domain and its characteristic function.
Citation:
A. A. Tatarkin, A. B. Shishkin, “Synthesis in the kernel of the three-way convolution operator”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 130–141
\Bibitem{TatShi21}
\by A.~A.~Tatarkin, A.~B.~Shishkin
\paper Synthesis in the kernel of the three-way convolution operator
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 193
\pages 130--141
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into807}
\crossref{https://doi.org/10.36535/0233-6723-2021-193-130-141}
Linking options:
https://www.mathnet.ru/eng/into807
https://www.mathnet.ru/eng/into/v193/p130
This publication is cited in the following 3 articles:
A. A. Tatarkin, A. B. Shishkin, “Exponential Synthesis in the Kernel of a q-Sided Convolution Operator”, J Math Sci, 282:4 (2024), 581
A. A. Tatarkin, A. B. Shishkin, “Eksponentsialnyi sintez v yadre operatora $q$-storonnei svertki”, Issledovaniya po lineinym operatoram i teorii funktsii. 50, Zap. nauchn. sem. POMI, 512, POMI, SPb., 2022, 191–222
Yu. S. Saranchuk, A. B. Shishkin, “General elementary solution of a homogeneous $q$-sided convolution type equation”, St. Petersburg Math. J., 34:4 (2023), 695–713
Citation in format AMSBIB
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