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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 849–860
DOI: https://doi.org/10.17377/semi.2016.13.067 (Mi semr717) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Differentical equations, dynamical systems and optimal control

On an identity for the iterated weighted spherical mean and its applications

S. M. Sitnikab, E. L. Shishkinac

a Voronezh Institute of the Ministry of Internal Affairs, pr. Patriotov, 53, Voronezh, 394065, Russia
b Peoples' Friendship University of Russia, M.-Maklaya str., 6, Moscow, 117198, Russia
c Voronezh State University, Universitetskaya pl. 1, Voronezh, 394000, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.067
Abstract: Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We generalize iterated spherical means to weighted ones based on generalized translation operators and consider applications to $B$-hyperbolic equations and transmission tomography problems.
Keywords: spherical means, weighted means, Àsgeirsson theorem, iterated means, $B$-hyperbolic equation, integral geometry, tomography.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-8215.2016.1
Received June 24, 2016, published October 14, 2016
Bibliographic databases:
Document Type: Article
UDC: 517.444
MSC: 35С15
Language: Russian
Citation: S. M. Sitnik, E. L. Shishkina, “On an identity for the iterated weighted spherical mean and its applications”, Sib. Èlektron. Mat. Izv., 13 (2016), 849–860
Citation in format AMSBIB
\Bibitem{SitShi16}
\by S.~M.~Sitnik, E.~L.~Shishkina
\paper On an identity for the iterated weighted spherical mean and its applications
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 849--860
\mathnet{http://mi.mathnet.ru/semr717}
\crossref{https://doi.org/10.17377/semi.2016.13.067}
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