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Conic injectivity sets for the Radon transformation on spheres


Authors: V. V. Volchkov and Vit. V. Volchkov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 5.
Journal: St. Petersburg Math. J. 27 (2016), 709-730
MSC (2010): Primary 44A12
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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Additional Information

V. V. Volchkov
Affiliation: Donetsk national university, 24 Universitetskaya str., Donetsk 83001, Ukraine
Email: valeriyvolchkov@gmail.com

Vit. V. Volchkov
Affiliation: Donetsk national university, 24 Universitetskaya str., Donetsk 83001, Ukraine

DOI: https://doi.org/10.1090/spmj/1413
Keywords: Conic sets, Radon transformation, Darboux equation, wave equation
Received by editor(s): December 16, 2014
Published electronically: July 26, 2016
Article copyright: © Copyright 2016 American Mathematical Society