Geodesic
Plane waves on a sphere and some applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 3, pp. 421-426 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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