Geodesic
A~generalization of the Funk--Hecke theorem to the case of hyperbolic spaces
Izvestiya. Mathematics , Tome 68 (2004) no. 5, pp. 1051-1061.

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The well-known Funk–Hecke theorem states that for integral operators whose kernels depend only on the distance between points in spherical geometry and where the integral is taken over the surface of a hypersphere, every surface spherical harmonic is an eigenvector. In this paper we extend this theorem to the case of non-compact Lobachevsky spaces. We compute the corresponding eigenvalue in some physically important cases. 
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T. V. Shtepina. A~generalization of the Funk--Hecke theorem to the case of hyperbolic spaces. Izvestiya. Mathematics , Tome 68 (2004) no. 5, pp. 1051-1061. http://geodesic.mathdoc.fr/item/IM2_2004_68_5_a7/

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