Geodesic
On an identity for the iterated weighted spherical mean and its applications
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 849-860

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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. 
@article{SEMR_2016_13_a83,
     author = {S. M. Sitnik and E. L. Shishkina},
     title = {On an identity for the iterated weighted spherical mean and its applications},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {849--860},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a83/}
}
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S. M. Sitnik; E. L. Shishkina. On an identity for the iterated weighted spherical mean and its applications. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 849-860. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a83/