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Izvestiya: Mathematics, 2013, Volume 77, Issue 2, Pages 223–252
DOI: https://doi.org/10.1070/IM2013v077n02ABEH002634 (Mi im7956) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Spherical means on two-point homogeneous spaces and applications

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University
English version PDF (470 kB) Citations (7)
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DOI: https://doi.org/10.1070/IM2013v077n02ABEH002634
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-à
12-01-00155-a
Received: 13.01.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 2, Pages 3–34
DOI: https://doi.org/10.4213/im7956
Bibliographic databases:
Document Type: Article
UDC: 517.988.28
MSC: 43A80, 53C35, 53C65
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:70
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