Geodesic
Spherical means on two-point homogeneous spaces and applications
Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 223-252

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We solve the following fundamental problems of integral geometry for certain integral transformations related to the spherical mean operator: obtain necessary and sufficient conditions for injectivity, describe the kernel in the case of non-injectivity, and find an inversion formula. Our results have unexpected applications to overdetermined interpolation problems in the theory of entire functions.
Keywords: spherical means, symmetric spaces
Mots-clés : Pompeiu transform, inversion formulae. 
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     author = {V. V. Volchkov and Vit. V. Volchkov},
     title = {Spherical means on two-point homogeneous spaces and applications},
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V. V. Volchkov; Vit. V. Volchkov. Spherical means on two-point homogeneous spaces and applications. Izvestiya. Mathematics , Tome 77 (2013) no. 2, pp. 223-252. http://geodesic.mathdoc.fr/item/IM2_2013_77_2_a0/