The Plancherel formula for the pseudo-riemannian space SL ( n , ) / GL ( n - 1 , )

G. Van Dijk; M. Poel

Compositio Mathematica (1986)

  • Volume: 58, Issue: 3, page 371-397
  • ISSN: 0010-437X

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Van Dijk, G., and Poel, M.. "The Plancherel formula for the pseudo-riemannian space $\mathrm {SL}(n, \mathbb {R}) / \mathrm {GL}(n - 1, \mathbb {R})$." Compositio Mathematica 58.3 (1986): 371-397. <http://eudml.org/doc/89775>.

@article{VanDijk1986,
author = {Van Dijk, G., Poel, M.},
journal = {Compositio Mathematica},
keywords = {pseudo-Riemannian symmetric space; generalized Gelfand pair; relative discrete series; rank one symmetric space; Plancherel formula},
language = {eng},
number = {3},
pages = {371-397},
publisher = {Martinus Nijhoff Publishers},
title = {The Plancherel formula for the pseudo-riemannian space $\mathrm \{SL\}(n, \mathbb \{R\}) / \mathrm \{GL\}(n - 1, \mathbb \{R\})$},
url = {http://eudml.org/doc/89775},
volume = {58},
year = {1986},
}

TY - JOUR
AU - Van Dijk, G.
AU - Poel, M.
TI - The Plancherel formula for the pseudo-riemannian space $\mathrm {SL}(n, \mathbb {R}) / \mathrm {GL}(n - 1, \mathbb {R})$
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 58
IS - 3
SP - 371
EP - 397
LA - eng
KW - pseudo-Riemannian symmetric space; generalized Gelfand pair; relative discrete series; rank one symmetric space; Plancherel formula
UR - http://eudml.org/doc/89775
ER -

References

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  1. [1] A. Borel: Représentations de groupes localement compacts, Lecture Notes in Mathematics, Vol. 276. Springer, Berlin etc. (1972). Zbl0242.22007MR414779
  2. [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). Zbl0327.22011MR460541
  3. [3] A. Erdelyi et al.: Higher Trancendental Functions, Vol. I. New York: McGraw-Hill (1953). Zbl0051.30303
  4. [4] A. Erdelyi et al.: Higher Transcendental Functions, Vol. II. New York: McGraw-Hill (1953). Zbl0052.29502
  5. [5] J. Faraut: Distributions sphériques sur les espaces hyperboliques, J. Math. Pures Appl.58 (1979) 369-444. Zbl0436.43011MR566654
  6. [6] T. Kengmana: Discrete series characters on non-Riemannian symmetric spaces, thesis, Harvard University, Cambridge (Mass.) (1984). Zbl0523.22014
  7. [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.). MR852659
  8. [8] K. Maurin and L. Maurin: Universelle umhüllende Algebra einer Lokal kompakten Gruppe und ihre selbstadjungierte Darstellungen. Anwendungen. Studia Math., 24 (1964) 227-243. Zbl0139.07801MR177065
  9. [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). Zbl0515.22012
  10. [10] E. Nelson: Analytic vectors. Ann. of Math.70 (1959) 572-615. Zbl0091.10704MR107176
  11. [11] W. Rossmann: Analysis on real hyperbolic spaces. J. Funct. Anal.30 (1978) 448-477. Zbl0395.22014MR518343
  12. [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). Zbl0564.43008MR761388
  13. [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. [14] G. Van Dijk: On generalized Gelfand pairs. Proc. Japan Acad. Sc.60, Ser. A(1984) 30-34 Zbl0555.43010MR751755

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