Relativity, spherical functions and the hypergeometric equation
Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 2, pp. 103-144.
Unterberger, André 1

1 Université de Reims, Mathématiques (UMR 6056), Moulin de la Housse, B.P.1039, 51687 REIMS Cedex 2 (France)
@article{AIHPA_1995__62_2_103_0,
     author = {Unterberger, Andr\'e},
     title = {Relativity, spherical functions and the hypergeometric equation},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {103--144},
     publisher = {Gauthier-Villars},
     volume = {62},
     number = {2},
     year = {1995},
     mrnumber = {1317183},
     zbl = {0834.43011},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1995__62_2_103_0/}
}
TY  - JOUR
AU  - Unterberger, André
TI  - Relativity, spherical functions and the hypergeometric equation
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1995
SP  - 103
EP  - 144
VL  - 62
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1995__62_2_103_0/
LA  - en
ID  - AIHPA_1995__62_2_103_0
ER  - 
%0 Journal Article
%A Unterberger, André
%T Relativity, spherical functions and the hypergeometric equation
%J Annales de l'I.H.P. Physique théorique
%D 1995
%P 103-144
%V 62
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1995__62_2_103_0/
%G en
%F AIHPA_1995__62_2_103_0
Unterberger, André. Relativity, spherical functions and the hypergeometric equation. Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 2, pp. 103-144. http://www.numdam.org/item/AIHPA_1995__62_2_103_0/

[1] R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Collection CEA, Paris, 1985. | Zbl

[2] J. Dieudonné, Calcul infinitésimal, Hermann, Paris, 1980. | MR | Zbl

[3] J. Faraut, Analyse harmonique sur les espaces hermitiens symétriques de rang un, CIMPA, Université de Nancy, 1980.

[4] R. Gangolli and V.S. Varadarajan, Harmonic Analysis of Spherical Functions on Real Reductive Groups, Springer-Verlag, Berlin, 1988. | MR | Zbl

[5] K.I. Gross and R.A. Kunze, Fourier Bessel Transforms and Holomorphic Discrete Series, Lecture Notes in Math., No. 266, 1972, pp. 79-122. | MR | Zbl

[6] K.I. Gross and R.A. Kunze, Bessel Functions and Representation Theory I, II, J. Funct. Anal., Vol. 22, 1976, pp. 73-105; ibid.,, Vol. 25, 1977, pp. 1-49. | MR | Zbl

[7] S. Helgason, Groups and Geometric Analysis, Acad. Press, New York, 1984. | MR | Zbl

[8] L. Jager, Fonctions de Mathieu et calcul de Klein-Gordon, Thèse, Université de Reims, 1994.

[9] A.W. Knapp, Representation Theory of Semi-Simple Groups, Princeton University Press, 1986. | MR | Zbl

[10] W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd edition, Springer-Verlag, Berlin, 1966. | MR | Zbl

[11] E. Mathieu, Mémoire sur le mouvement vibratoire d'une membrane de forme elliptique, Journal de Liouville, Vol. 13, 1968, p. 137. | EuDML | JFM | Numdam

[12] W. Miller, Symmetry and separation of variables, Addision-Wesley, 1977. | MR | Zbl

[13] J. Nourrigat, Méthodes asymptotiques, Cours de maîtrise, Université de Reims, 1990 (to appear).

[14] L. Pukanszky, The Plancherel Formula for the Universal Covering Group of SL(R, 2), Math. Annalen, Vol. 156, 1964, pp. 96-143. | EuDML | MR | Zbl

[15] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Acad. Press, 1975.

[16] L. Schwartz, Théorie des distributions,, Vol. 2, Hermann, Paris, 1959. | MR

[17] A. Unterberger, L'oscillateur relativiste et les fonctions de Mathieu, Bull. Soc. Math. France, Tome 121, No. 4, 1993, pp. 479-508. | EuDML | Numdam | MR | Zbl

[18] A. Unterberger, Quantification relativiste, Mémoires de la Soc. Math. France, No. 44-45, Paris, 1991. | EuDML | Numdam | MR | Zbl

[19] A. Unterberger, Les opérateurs métadifférentiels, Lectures Notes in Physics, No. 126, 1980, pp. 205-241. | MR | Zbl

[20] A. Unterberger and J. Unterberger, La série discrète de SL (2, R) et les opérateurs pseudo-différentiels sur une demi-droite, Ann.Sci. Ec. Norm. Sup., Tome 17, 1984, pp. 83-116. | EuDML | Numdam | MR | Zbl

[21] Z.X. Wang and D.R. Guo, Special Functions, World Scientific (Singapore), 1989. | MR | Zbl

[22] E.T. Whittaker and G.N. Watson, A course of modern Analysis, 4th edition, Cambridge Univ. Press, 1965. | MR