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On functions with given spherical means on symmetric spaces

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Abstract

The inversion problem for a local Pompeiu transformation of rank one on sym- metric spaces X of the noncompact type is studied. The reconstruction of a function defined in the ball B R ⊂ X by its averages on balls of two fixed radii lying in B R is obtained.

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Authors and Affiliations

  1. Donetsk National University, 24, Universitetskaya Str., Donetsk, 34001, Ukraine

    Vitalii Vladimirovich Volchkov

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  1. Vitalii Vladimirovich Volchkov
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Correspondence to Vitalii Vladimirovich Volchkov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 7, No. 4, pp. 453–466, October–November, 2010.

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Vladimirovich Volchkov, V. On functions with given spherical means on symmetric spaces. J Math Sci 175, 402–412 (2011). https://doi.org/10.1007/s10958-011-0354-2

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  • DOI: https://doi.org/10.1007/s10958-011-0354-2

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