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Distributions a support compact et representations unitaires

Dominique Manchon
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Abstract

Dans cet article nous precisons les notions de representations unitaires fortement tracables et de front d'onde d'une representation unitaire, toutes deux introduites par Roger Howe. Nous montrons que pour toute distribution $ϕ$ a support compact sur un groupe de Lie connexe dont le front d'onde ne rencontre pas l'oppose du front d'onde de la representation $π$ l'operateur $π(ϕ)$ est regularisant. De plus, sous les memes hypotheses cet operateur est a trace si la representation est fortement tracable. Dans le cas ou la representation est irreductible et associee par la methode des orbites a une orbite fermee et temperee, nous montrons qu'elle est fortement tracable et nous etendons la formule des caracteres aux operateurs $π(ϕ)$ pour les distributions $ϕ$ a support compact dont le front d'onde verifie la condition de transversalite ci-dessus.

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Dominique Manchon. 1998-09-01. Distributions a support compact et representations unitaires. https://arxiv.org/abs/math/9809005

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