Conic injectivity sets for the Radon transformation on spheres

Volchkov, V.; Volchkov, Vit.

doi:10.1090/spmj/1413

Conic injectivity sets for the Radon transformation on spheres
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by V. V. Volchkov and Vit. V. Volchkov
Translated by: A. Plotkin

St. Petersburg Math. J. 27 (2016), 709-730

DOI: https://doi.org/10.1090/spmj/1413

Published electronically: July 26, 2016

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Abstract:

The problem under study concerns description of nonzero functions that have zero integrals over all spheres with centers in a given set. For the corresponding integral transformation (Radon transformation on spheres), the kernel is described, and sharp uniqueness theorems are obtained. Applications of the main results to partial differential equations are considered: new uniqueness theorems are proved for the Darboux equation and the wave equation.

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