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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Fonctions sphériques des espaces symétriques compacts
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by Jean-Louis Clerc PDF
Trans. Amer. Math. Soc. 306 (1988), 421-431 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • 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