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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)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 1, Pages 43–62
DOI: https://doi.org/10.4213/im8200
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. RAN. Ser. Mat., 79:1 (2015), 43–62; Izv. Math., 79:1 (2015), 40–59
Citation in format AMSBIB
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  • 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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    References:43
    First page:31
     
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