This article is cited 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

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.

UDC: 517.5

MSC: 33C55, 43A90, 44A15, 53C65

Received: 16.12.2013

DOI: 10.4213/im8200

 English version: Izvestiya: Mathematics, 2015, 79:1, 40–59

Bibliographic databases:

• 
• 
• 
• 
• 
•