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A Paley-Wiener theorem for the spherical Laplace transform on causal symmetric spaces of rank 1
Author(s):
Nils
Byrial
Andersen;
Gestur
Ólafsson
Journal:
Proc. Amer. Math. Soc.
129
(2001),
173-179.
MSC (2000):
Primary 43A85, 22E30;
Secondary 43A90, 33C60
Posted:
June 14, 2000
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Abstract:
We formulate and prove a topological Paley-Wiener theorem for the normalized spherical Laplace transform defined on the rank 1 causal symmetric spaces  , for  .
References:
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- [BS]
- E. P. van den Ban and H. Schlichtkrull, Expansions for Eisenstein integrals on semisimple symmetric spaces, Ark. Mat. 35 (1997), 59-86. MR 98e:22003
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- Erdélyi ét al, Higher Transcendental Functions, Volume I, McGraw-Hill, New York, 1973.
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- J. Faraut, J. Hilgert and G. Ólafsson, Spherical functions on ordered symmetric spaces, Ann. Inst. Fourier 44 (1994), 927-965. MR 96a:43012
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- S. Helgason, Groups and Geometric Analysis, Academic Press, Orlando, 1984. MR 86c:22017
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- S. Helgason, Geometric Analysis on Symmetric Spaces, Mathematical Surveys and Monographs. Vol. 39, American Mathematical Society, Providence, Rhode Island, 1994. MR 96h:43009
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- J. Hilgert and G. Ólafsson, Causal Symmetric Spaces, Geometry and Harmonic Analysis, Perspectives in Mathematics , Vol. 18, Academic Press, San Diego, 1997. MR 97m:43006
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- M. Mizony, Une transformation de Laplace-Jacobi, SIAM J. Math. 14 (1983), 987-1003. MR 85e:44002
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- G. Ólafsson, Spherical Functions and Spherical Laplace Transform on Ordered Symmetric Spaces, Preprint (see http://math.lsu.edu/
 olafsson/publicat.htm), 1997. - [O2]
- G. Ólafsson, Open problems in Harmonic Analysis on Causal Symmetric Spaces, Ed: J. Hilgert, J. D. Lawson, K-H Neeb and E. B. Vinberg; Positivity in Lie theory, Open Problems, De Gruyter Expositions in Mathematics, Berlin, 1998, 249-270. MR 99h:43021
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Additional Information:
Nils
Byrial
Andersen
Affiliation:
Institut de Mathématiques, Analyse Algèbrique, Université Pierre et Marie Curie, Case 82, Tour 46-0, 3$^{e}$ étage, 4, place Jussieu, F-75252 Paris Cedex 05, France
Address at time of publication:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email:
byrial@math.jussieu.fr, byrial@math.lsu.edu
Gestur
Ólafsson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email:
olafsson@math.lsu.edu
DOI:
10.1090/S0002-9939-00-05475-7
PII:
S 0002-9939(00)05475-7
Received by editor(s):
December 9, 1998
Received by editor(s) in revised form:
March 22, 1999
Posted:
June 14, 2000
Additional Notes:
The first author was supported by a postdoc fellowship from the European Commission within the European TMR Network ``Harmonic Analysis" 1998-2001 (Contract ERBFMRX-CT97-0159). The second author was supported by LEQSF grant (1996-99)-RD-A-12.
Communicated by:
Roe Goodman
Copyright of article:
Copyright
2000,
American Mathematical Society
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