This article is cited in 8 papers

Spherical means on two-point homogeneous spaces and applications

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University

Abstract: 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, Pompeiu transform, symmetric spaces, inversion formulae.

UDC: 517.988.28

MSC: 43A80, 53C35, 53C65

Received: 13.01.2012

DOI: 10.4213/im7956

 English version: Izvestiya: Mathematics, 2013, 77:2, 223–252

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