This article is cited in 16 papers

Injectivity sets for the Radon transform over a sphere

V. V. Volchkov

Donetsk National University

Abstract: This paper contains a solution of the problem of describing the kernel of the Radon transform over a sphere with respect to sets with spherical symmetry. This solution enabled us, in particular, to characterize all injectivity sets of this type. The technique used in the proofs enabled us to obtain other exact results concerning spherical means, namely, new two-radii theorems and a uniqueness theorem.

MSC: 44A12, 43A85, 42A38, 42B10, 43A90, 47G10, 45P05, 31A05

Received: 01.10.1997

DOI: 10.4213/im248

 English version: Izvestiya: Mathematics, 1999, 63:3, 481–493

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