A Paley-Wiener theorem for the spherical Laplace transform on causal symmetric spaces of rank 1
HTML articles powered by AMS MathViewer
- by Nils Byrial Andersen and Gestur Ólafsson PDF
- Proc. Amer. Math. Soc. 129 (2001), 173-179 Request permission
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 $n\ge 2$.References
- Erik P. van den Ban and Henrik Schlichtkrull, Expansions for Eisenstein integrals on semisimple symmetric spaces, Ark. Mat. 35 (1997), no. 1, 59–86. MR 1443036, DOI 10.1007/BF02559593
- Erdélyi ét al, Higher Transcendental Functions, Volume I, McGraw-Hill, New York, 1973.
- J. Faraut, J. Hilgert, and G. Ólafsson, Spherical functions on ordered symmetric spaces, Ann. Inst. Fourier (Grenoble) 44 (1994), no. 3, 927–965 (English, with English and French summaries). MR 1303888
- Sigurdur Helgason, Groups and geometric analysis, Pure and Applied Mathematics, vol. 113, Academic Press, Inc., Orlando, FL, 1984. Integral geometry, invariant differential operators, and spherical functions. MR 754767
- Sigurdur Helgason, Geometric analysis on symmetric spaces, Mathematical Surveys and Monographs, vol. 39, American Mathematical Society, Providence, RI, 1994. MR 1280714, DOI 10.1090/surv/039
- Joachim Hilgert and Gestur Ólafsson, Causal symmetric spaces, Perspectives in Mathematics, vol. 18, Academic Press, Inc., San Diego, CA, 1997. Geometry and harmonic analysis. MR 1407033
- Michel Mizony, Une transformation de Laplace-Jacobi, SIAM J. Math. Anal. 14 (1983), no. 5, 987–1003 (French, with English summary). MR 711179, DOI 10.1137/0514078
- G. Ólafsson, Spherical Functions and Spherical Laplace Transform on Ordered Symmetric Spaces, Preprint (see http://math.lsu.edu/ $\widetilde {\,\,}$olafsson/publicat.htm), 1997.
- Gestur Ólafsson, Open problems in harmonic analysis on causal symmetric spaces, Positivity in Lie theory: open problems, De Gruyter Exp. Math., vol. 26, de Gruyter, Berlin, 1998, pp. 249–270. MR 1648706
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
- MR Author ID: 133515
- Email: olafsson@math.lsu.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 173-179
- MSC (2000): Primary 43A85, 22E30; Secondary 43A90, 33C60
- DOI: https://doi.org/10.1090/S0002-9939-00-05475-7
- MathSciNet review: 1695108