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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 849–860 (Mi semr717)  

This article is cited in 4 scientific papers (total in 4 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

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


DOI: https://doi.org/10.17377/semi.2016.13.067

Full text: PDF file (187 kB)
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UDC: 517.444
MSC: 35С15
Received June 24, 2016, published October 14, 2016

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. L. Shishkina, S. M. Sitnik, “On fractional powers of Bessel operators”, J. Inequal. Spec. Funct., 8:1, SI (2017), 49–67  mathscinet  isi
    2. S. M. Sitnik, E. L. Shishkina, “O drobnykh stepenyakh operatora Besselya na poluosi”, Sib. elektron. matem. izv., 15 (2018), 1–10  mathnet  crossref
    3. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    4. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
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