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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fonctions sphériques des espaces symétriques compacts


Author: Jean-Louis Clerc
Journal: Trans. Amer. Math. Soc. 306 (1988), 421-431
MSC: Primary 43A90; Secondary 22E46
DOI: https://doi.org/10.1090/S0002-9947-1988-0927699-4
MathSciNet review: 927699
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Abstract: An integral formula, similar to Harish-Chandra's formula for spherical functions on a noncompact Riemannian symmetric space $ G/K$ is given for the spherical functions of the compact dual $ U/K$. As a consequence, an asymptotic expansion, as the parameter tends to infinity, is obtained, by using the (complex) stationary phase method.

RÉSUMÉ. On démontre une formule intégrale pour les fonctions sphériques d'un espace symétrique de type compact $ U/K$, analogue de la formule d'Harish-Chandra pour le dual non-compact $ G/K$. En conséquence on obtient un équivalent asymptotique lorsque le paramètre tend vers l'infini, en utilisant la méthode de la phase stationnaire complexe.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0927699-4
Article copyright: © Copyright 1988 American Mathematical Society