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Izvestiya: Mathematics, 2015, Volume 79, Issue 1, Pages 40–59
DOI: https://doi.org/10.1070/IM2015v079n01ABEH002733 (Mi im8200) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Description of the kernel of the generalized Minkowski transform on the sphere

V. V. Volchkov, Vit. V. Volchkov, I. M. Savost'yanova

Donetsk National University
English version PDF (355 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/IM2015v079n01ABEH002733
Abstract: We study the generalized Minkowski transform that sends functions on a sphere to their weighted integrals over closed geodesics. We solve the problem of describing the kernel of this transform and some related classes of functions. As an application, we obtain new and definitive uniqueness theorems for functions on a sphere with zero weighted averages over great circles.
Keywords: spherical means, Minkowski transform, Legendre functions.
Received: 16.12.2013
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 33C55, 43A90, 44A15, 53C65
Language: English
Original paper language: Russian
Citation: V. V. Volchkov, Vit. V. Volchkov, I. M. Savost'yanova, “Description of the kernel of the generalized Minkowski transform on the sphere”, Izv. Math., 79:1 (2015), 40–59
Citation in format AMSBIB
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\by V.~V.~Volchkov, Vit. V. Volchkov, I.~M.~Savost'yanova
\paper Description of the kernel of the generalized Minkowski transform on the sphere
\jour Izv. Math.
\yr 2015
\vol 79
\issue 1
\pages 40--59
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  • https://www.mathnet.ru/eng/im8200
  • https://doi.org/10.1070/IM2015v079n01ABEH002733
  • https://www.mathnet.ru/eng/im/v79/i1/p43
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Èçâåñòèÿ Ðîññèéñêîé àêàäåìèè íàóê. Ñåðèÿ ìàòåìàòè÷åñêàÿ Izvestiya: Mathematics
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    Abstract page:471
    Russian version PDF:190
    English version PDF:13
    References:54
    First page:31
     
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