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FARAUT, J., Distributions sphériques sur les espaces hyperboliques, J. Math. Pures Appl. 58, 369–444 (1979).
GELFAND, I.M., GRAEV, M.I. and VILENKIN, N.Y., Generalized Functions vol. 5: Integral Geometry and Representation Theory, Academic Press, New-York-London 1966.
GODEMENT, R., Introduction aux travaux de A. Selberg, Séminaire Bourbaki, t.9, exp. 144 (1956/57).
HARISH-CHANDRA, Collected Papers, 4 volumes, Springer-Verlag, Berlin etc. 1983.
HARISH-CHANDRA, Spherical functions on a semisimple Lie group I,II Collected Papers, volume 2 (1983).
KOSTERS, M.T., Spherical distributions on rank one symmetric spaces, Phd. Thesis, University of Leiden (1983).
KOSTERS, W.A., Harmonic analysis on symmetric spaces, Phd. Thesis, University of Leiden (1985).
LIMIM, N., NIEDERLE, J. and RACZKA, R., Eigenfunction expansions associated with the second-order invariant operator on hyperboloids and cones, III, J. Math. Phys. 8, 1079–1093 (1967).
MATSUMOTO, S., The Plancherel formula for a pseudo-Riemannian symmetric space, Hiroshima Math. J. 8, 181–193 (1978).
MOLCANOV, V.F., The Plancherel formula for hyperboloids, Proceedings of the Steklov Institute of Mathematics, 2, 63–83 (1981).
MOLCANOV, V.F., Harmonic analysis on the pseudo-Riemannian symmetric spaces of the group SL(2,]R), Math. USSR Sbornik 46, no.4, 493–505 (1983).
MOLCANOV, V.F., The Plancherel formula for the pseudo-Riemannian space SL(3,]R)/GL(2,]R), Sibirsk Math. J. 23, 142–151 (1982) (Russian).
NIEDERLE, J., Decomposition of discrete most degenerate representations of SO0(p,q) when restricted to representations of SO0(p,q-1) or SO0(p-l,q), J. Math. Phys. 8, 1921–1930 (1967)
ROSSMANN, W., Analysis on real hyperbolic spaces, J. Funct. Anal. 30, 448–477 (1978).
SCHEMPP, W., DRESELER, B., Einführung in die harmonische Analyse, B.G. Teubner, Stuttgart, 1980.
SCHWARTZ, L., Sousespaces Hilbertiéns d'espaces vectoriels topologiques et noyaux associés, J. Anal. Math. 13, 115–256 (1964).
SEGAL, I.E., The two-sided regular representation of a unimodular locally compact group, Annals of Math. 51, 293–298 (1950).
SHINTANI, T., On the decomposition of the regular representation of the Lorentz group on a hyperboloid of one sheet, Proc. Japan Acad. 43, 1–5 (1967).
STRICHARTZ, R.S., Harmonic analysis on hyperboloids, J. Funct. Anal. 12, 341–383 (1973).
TAKAHASHI, R., Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France 91, 289–433 (1962).
THOMAS, E.G.F., The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs, Functional Analysis: Surveys and results III, K.D. Bierstedt and B. Fuchsteiner (eds.), Elsevier Science Publishers B.V. (North Holland) (1984).
VAN DIJK, G., POEL, M., The Plancherel formula for the pseudo-Riemannian space SL(n,]R)/GL(n-l,]R), preprint, Univ. of Leiden (1984), to appear in Comp. Math..
VAN DIJK, G., On a class of generalized Gelfand pairs, Report nr. 18, Mathematical Institute, Univ. of Leiden (1985).
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van Dijk, G. (1986). Harmonic analysis on rank one symmetric spaces. In: Barut, A.O., Doebner, H.D. (eds) Conformal Groups and Related Symmetries Physical Results and Mathematical Background. Lecture Notes in Physics, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540171630_85
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DOI: https://doi.org/10.1007/3540171630_85
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