Geodesic
The Radon--Kipriyanov Transform of the Generalized Spherical Mean of a Function
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 118-132

Voir la notice de l'article provenant de la source Math-Net.Ru

A formula relating the Radon transform of functions of spherical symmetries to the Radon–Kipriyanov transform $K_\gamma$ for a natural multi-index $\gamma$ is given. For an arbitrary multi-index $\gamma$, formulas for the representation of the $K_\gamma$-transform of a radial function as fractional integrals of Erdelyi–Kober integral type and of Riemann–Liouville integral type are proved. The corresponding inversion formulas are obtained. These results are used to study the inversion of the Radon–Kipriyanov transform of the generalized (generated by a generalized shift) spherical mean values of functions that belong to a weighted Lebesgue space and are even with respect to each of the weight variables.
Mots-clés : Radon transform
Keywords: Radon–Kipriyanov transform, radial function, multiaxial spherical symmetry, generalized spherical mean, fractional integral, fractional derivative. 
@article{MZM_2016_100_1_a8,
     author = {L. N. Lyakhov},
     title = {The {Radon--Kipriyanov} {Transform} of the {Generalized} {Spherical} {Mean} of a {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {118--132},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a8/}
}
TY  - JOUR
AU  - L. N. Lyakhov
TI  - The Radon--Kipriyanov Transform of the Generalized Spherical Mean of a Function
JO  - Matematičeskie zametki
PY  - 2016
SP  - 118
EP  - 132
VL  - 100
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a8/
LA  - ru
ID  - MZM_2016_100_1_a8
ER  - 
%0 Journal Article
%A L. N. Lyakhov
%T The Radon--Kipriyanov Transform of the Generalized Spherical Mean of a Function
%J Matematičeskie zametki
%D 2016
%P 118-132
%V 100
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a8/
%G ru
%F MZM_2016_100_1_a8
L. N. Lyakhov. The Radon--Kipriyanov Transform of the Generalized Spherical Mean of a Function. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 118-132. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a8/