Description of the kernel of the generalized Minkowski transform on the sphere
Izvestiya. Mathematics , Tome 79 (2015) no. 1, pp. 40-59
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{IM2_2015_79_1_a2,
author = {V. V. Volchkov and Vit. V. Volchkov and I. M. Savost'yanova},
title = {Description of the kernel of the generalized {Minkowski} transform on the sphere},
journal = {Izvestiya. Mathematics },
pages = {40--59},
publisher = {mathdoc},
volume = {79},
number = {1},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_1_a2/}
}
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V. V. Volchkov; Vit. V. Volchkov; I. M. Savost'yanova. Description of the kernel of the generalized Minkowski transform on the sphere. Izvestiya. Mathematics , Tome 79 (2015) no. 1, pp. 40-59. http://geodesic.mathdoc.fr/item/IM2_2015_79_1_a2/