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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 1, Pages 43–62 (Mi izv8200)  

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

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.

DOI: https://doi.org/10.4213/im8200

Full text: PDF file (562 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:1, 40–59

Bibliographic databases:

UDC: 517.5
MSC: 33C55, 43A90, 44A15, 53C65
Received: 16.12.2013

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/10.4213/im8200
  • http://mi.mathnet.ru/eng/izv/v79/i1/p43

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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