Geodesic
Plane waves on a~sphere and some applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 3, pp. 421-426

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

Fourier analysis on a sphere of dimension $d\geqslant 2$ is developed in a form that recalls Fourier analysts in flat space to the maximal extent possible. Plane waves – the kernels of the corresponding integral transforms – are generalized functions, for which a regularization is defined; completeness relations, finite-difference equations, and a composition theorem are found. In the case $d=4$, these functions are used for the transition to the Euclidean expressions in the commutator functions of field theory with a curved momentum space; for $d=3$, they are used to describe a class of states in a Coulomb field. 
@article{TMF_1980_45_3_a11,
     author = {I. P. Volobuev},
     title = {Plane waves on a~sphere and some applications},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {421--426},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_45_3_a11/}
}
TY  - JOUR
AU  - I. P. Volobuev
TI  - Plane waves on a~sphere and some applications
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 421
EP  - 426
VL  - 45
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_45_3_a11/
LA  - ru
ID  - TMF_1980_45_3_a11
ER  - 
%0 Journal Article
%A I. P. Volobuev
%T Plane waves on a~sphere and some applications
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 421-426
%V 45
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1980_45_3_a11/
%G ru
%F TMF_1980_45_3_a11
I. P. Volobuev. Plane waves on a~sphere and some applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 3, pp. 421-426. http://geodesic.mathdoc.fr/item/TMF_1980_45_3_a11/