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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 2, Pages 3–34 (Mi izv7956)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00384-
12-01-00155-a


DOI: https://doi.org/10.4213/im7956

Full text: PDF file (733 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:2, 223–252

Bibliographic databases:

UDC: 517.988.28
MSC: 43A80, 53C35, 53C65
Received: 13.01.2012

Citation: V. V. Volchkov, Vit.V.Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. RAN. Ser. Mat., 77:2 (2013), 3–34; Izv. Math., 77:2 (2013), 223–252

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