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

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. © 2016 Shishkina, E.L., Sitnik, S.M.

Authors
Shishkina E.L.1 , Sitnik S.M. 2, 3
Publisher
Sobolev Institute of Mathematics
Language
Russian
Pages
849-860
Status
Published
Volume
13
Year
2016
Organizations
  • 1 Voronezh State University, Universitetskaya pl. 1, Voronezh, 394000, Russian Federation
  • 2 Voronezh Institute of the Ministry of Internal Affairs, pr. Patriotov, 53, Voronezh, 394065, Russian Federation
  • 3 Peoples' Friendship University of Russia, M. - Maklaya str., 6, Moscow, 117198, Russian Federation
Keywords
B-hyperbolic equation; Integral geometry; Iterated means; Spherical means; Tomography; Weighted means; Àsgeirsson theorem
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4304/