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A Paley-Wiener theorem for the spherical Laplace transform on causal symmetric spaces of rank 1


Authors: Nils Byrial Andersen and Gestur Ólafsson
Journal: Proc. Amer. Math. Soc. 129 (2001), 173-179
MSC (2000): Primary 43A85, 22E30; Secondary 43A90, 33C60
Published electronically: June 14, 2000
MathSciNet review: 1695108
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Abstract | References | Similar Articles | Additional Information

Abstract:

We formulate and prove a topological Paley-Wiener theorem for the normalized spherical Laplace transform defined on the rank 1 causal symmetric spaces $\mathcal{M} = SO _{o} (1,n)/SO_{o}(1,n-1)$, for $n\ge 2$.


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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: http://dx.doi.org/10.1090/S0002-9939-00-05475-7
Received by editor(s): December 9, 1998
Received by editor(s) in revised form: March 22, 1999
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society