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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) Russian version article
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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
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. Math., 77:2 (2013), 223–252
Citation in format AMSBIB
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\by V.~V.~Volchkov, Vit. V. Volchkov
\paper Spherical means on two-point homogeneous spaces and applications
\jour Izv. Math.
\yr 2013
\vol 77
\issue 2
\pages 223--252
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Linking options:
  • https://www.mathnet.ru/eng/im7956
  • https://doi.org/10.1070/IM2013v077n02ABEH002634
  • https://www.mathnet.ru/eng/im/v77/i2/p3
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Èçâåñòèÿ Ðîññèéñêîé àêàäåìèè íàóê. Ñåðèÿ ìàòåìàòè÷åñêàÿ Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:756
    Russian version PDF:217
    English version PDF:18
    References:75
    First page:18
     
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