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Fonctions holomorphes à croissance modérée et vecteurs distributions

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L’espace des vecteurs distributions d’une représentation de la série discrète holomorphe scalaire d’un domaine borné symétrique s’identifie à l’espace des fonctions holomorphes à croissance modérée. C’est le principal résultat de cet article. Nous en donnons une application à la transformation de Hankel et aux développements en série de fonctions de Laguerre de plusieurs variables.

Abstract.

The space of distribution vectors of a holomorphic discrete series representation of scalar type can be identified to a space of holomorphic functions with moderate growth. This is the main result of the paper. We give an application of it to the Hankel transform and to multivariate Laguerre series expansions.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060, Tunis, Tunisie

    Houcine Chébli

  2. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013, Paris, France

    Jacques Faraut

Authors
  1. Houcine Chébli
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  2. Jacques Faraut
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Correspondence to Jacques Faraut.

Additional information

Mathematics Subject Classification (2000): 32M15, 22E46

in final form: 19 January 2004

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Chébli, H., Faraut, J. Fonctions holomorphes à croissance modérée et vecteurs distributions. Math. Z. 248, 544–565 (2004). https://doi.org/10.1007/s00209-004-0669-5

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  • DOI: https://doi.org/10.1007/s00209-004-0669-5

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