The Plancherel formula for the pseudo-riemannian space SL (n,ℝ)/ GL (n-1,ℝ)
Compositio Mathematica, Tome 58 (1986) no. 3, pp. 371-397. 
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     author = {Van Dijk, G. and Poel, M.},
     title = {The {Plancherel} formula for the pseudo-riemannian space $\mathrm {SL}(n, \mathbb {R}) / \mathrm {GL}(n - 1, \mathbb {R})$},
     journal = {Compositio Mathematica},
     pages = {371--397},
     publisher = {Martinus Nijhoff Publishers},
     volume = {58},
     number = {3},
     year = {1986},
     mrnumber = {846911},
     zbl = {0593.43009},
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     url = {http://archive.numdam.org/item/CM_1986__58_3_371_0/}
}
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Van Dijk, G.; Poel, M. The Plancherel formula for the pseudo-riemannian space $\mathrm {SL}(n, \mathbb {R}) / \mathrm {GL}(n - 1, \mathbb {R})$. Compositio Mathematica, Tome 58 (1986) no. 3, pp. 371-397. http://archive.numdam.org/item/CM_1986__58_3_371_0/

[1] A. Borel: Représentations de groupes localement compacts, Lecture Notes in Mathematics, Vol. 276. Springer, Berlin etc. (1972). | MR | Zbl

[2] P. Cartier: Vecteurs différentiables dans les représentations unitaires des groupes de Lie, Lecture Notes in Mathematics, Vol. 514, 20-33. Springer, Berlin etc. (1976). | Numdam | MR | Zbl

[3] A. Erdelyi et al.: Higher Trancendental Functions, Vol. I. New York: McGraw-Hill (1953). | Zbl

[4] A. Erdelyi et al.: Higher Transcendental Functions, Vol. II. New York: McGraw-Hill (1953). | Zbl

[5] J. Faraut: Distributions sphériques sur les espaces hyperboliques, J. Math. Pures Appl. 58 (1979) 369-444. | MR | Zbl

[6] T. Kengmana: Discrete series characters on non-Riemannian symmetric spaces, thesis, Harvard University, Cambridge (Mass.) (1984).

[7] M.T. Kosters and G. Van Dijk: Spherical distributions on the pseudo-Riemannian space SL(n, R)/GL(n-1, R), Report no 23, University of Leiden, 1984 (to appear in J. Funct. Anal.). | MR

[8] K. Maurin and L. Maurin: Universelle umhüllende Algebra einer Lokal kompakten Gruppe und ihre selbstadjungierte Darstellungen. Anwendungen. Studia Math., 24 (1964) 227-243. | MR | Zbl

[9] V.F. Molčanov: The Plancherel formula for the pseudo-Riemannian space SL(3, R)/GL(2, R). Sibirsk Math. J. 23 (1982) 142-151 (Russian). | Zbl

[10] E. Nelson: Analytic vectors. Ann. of Math. 70 (1959) 572-615. | MR | Zbl

[11] W. Rossmann: Analysis on real hyperbolic spaces. J. Funct. Anal. 30 (1978) 448-477. | MR | Zbl

[12] E.G.F. Thomas: The theorem of Bochner-Schwartz-Godement for generalized Gelfand pairs. In: K.D. Bierstedt and B. Fuchsteiner (eds.), Functional Analysis: Surveys and recent results III, Elseviers Science Publishers B.V. (North Holland) (1984). | MR | Zbl

[13] E.P. Van Den Ban: Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula. Report PM-R 8409, Centre for Mathematics and Computer Science, Amsterdam (1984).

[14] G. Van Dijk: On generalized Gelfand pairs. Proc. Japan Acad. Sc. 60, Ser. A(1984) 30-34 | MR | Zbl