Support d’asymptotiques et croissance des fonctions propres sur un espace symétrique semi-simple |
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Authors: | Jacques Carmona |
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Affiliation: | Institut de Mathématiques de Luminy, UPR 9016 du CNRS, Faculté des Sciences de Luminy, 163, Avenue de Luminy, Case 907, 13288 Marseille Cedex 09, France |
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Abstract: | We associate several distribution boundary values to an eigenfunction with moderate growth on a riemannian symmetric space G/K; the associated character of the algebra D(G/K) of invariant differential operators is allowed to be non-regular. We prove results on the support of these boundary values. These allow us to recover the theorems of Matsuki-Oshima and Oshima on the equivalence between growth of an eigenfunction and limitations on the supports of its boundary values. Our approach is based on an asymptotic analysis that makes no use of hyperfunction theory. |
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Keywords: | 20C99 22E30 |
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