Geodesic
Spherical functions on hyperboloids
Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 119-139 
V. F. Molchanov. Spherical functions on hyperboloids. Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 119-139. http://geodesic.mathdoc.fr/item/SM_1976_28_2_a0/
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     title = {Spherical functions on hyperboloids},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Spherical (zonal) functions on the hyperboloid $-x_1^2-\dots-x_p^2+x_{p+1}^2+\dots+x_{p+q}^2=1$ corresponding to unitary representations of the group $SO(p,q)$ connected with a cone (RZhMat., 1970, 7B710) are defined and computed. Bibliography: 15 titles.

[1] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, Moskva, 1958

[2] I. M. Gelfand, G. E. Shilov, Prostranstva osnovnykh i obobschennykh funktsii, Fizmatgiz, Moskva, 1958

[3] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatgiz, Moskva, 1962

[4] F. A. Berezin, “Operatory Laplasa na poluprostykh gruppakh Li”, Trudy Mosk. matem. ob-va, VI (1957), 371–463 | MR

[5] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, izd-vo «Nauka», Moskva, 1965 | MR

[6] N. Burbaki, Integrirovanie (vektornoe integrirovanie, mera Khaara, svertka i predstavleniya), izd-vo «Nauka», Moskva, 1970 | MR

[7] G. E. Shilov, Matematicheskii analiz (vtoroi spetsialnyi kurs), izd-vo «Nauka», Moskva, 1965 | MR

[8] S. Khelgason, Differentsialnaya geometriya i simmetricheskie prostranstva, izd-vo «Mir», Moskva, 1964

[9] Zh. Trev, Lektsii po lineinym uravneniyam v chastnykh proizvodnykh s postoyannymi koeffitsientami, izd-vo «Mir», Moskva, 1965

[10] A. Tengstrand, “Distributions invariant under an orthogonal group of arbitrary signature”, Math. Scand., 8 (1960), 201–218 | MR | Zbl

[11] S. Bokhner, U. T. Martin, Funktsii mnogikh kompleksnykh peremennykh, IL, Moskva, 1951

[12] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii (gipergeometricheskaya funktsiya, funktsii Lezhandra), izd-vo «Nauka», Moskva, 1965

[13] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, Moskva, 1963

[14] V. F. Molchanov, “Analog formuly Plansherelya dlya giperboloidov”, DAN SSSR, 183:2 (1968), 288–291 | Zbl

[15] V. F. Molchanov, “Predstavleniya psevdoortogonalnoi gruppy, svyazannye s konusom”, Matem. sb., 81 (123) (1970), 358–375 | Zbl