Geodesic
Fourier-Laplace series on the sphere
Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Tome 15 (1977), pp. 83-130.

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One presents the results which are presently known in the theory of Fourier–Laplace series on a $k$-dimensional ($k\ge3$) sphere. 
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     author = {L. V. Zhizhiashvili and S. B. Topuriya},
     title = {Fourier-Laplace series on the sphere},
     journal = {Itogi nauki i tehniki. Seri\^a, Matemati\v{c}eskij analiz},
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     url = {http://geodesic.mathdoc.fr/item/INTM_1977_15_a1/}
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L. V. Zhizhiashvili; S. B. Topuriya. Fourier-Laplace series on the sphere. Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Tome 15 (1977), pp. 83-130. http://geodesic.mathdoc.fr/item/INTM_1977_15_a1/