On the Hermite polynomials of a matrix argument. (Sur les polynômes d’Hermite d’une variable matricielle.) (French) Zbl 1002.43007
Summary: We define Hermite polynomials of a matrix argument. We use the coefficients of the “essential representation” of the affine group of transformations of \(\mathbb{R}^m\) to prove some important properties of those polynomials and their associated functions.
MSC:
43A80 | Analysis on other specific Lie groups |
References:
[1] | Akkouchi, M.; Bakali, A.; Daâmache, T., Groupe affine et polynômes d’Hermite, Math. Rech. Appl., 3 (2000) · Zbl 1018.33006 |
[2] | A. Bakali, Analyse harmonique sur les groupes \(ax b\); A. Bakali, Analyse harmonique sur les groupes \(ax b\) |
[3] | Duflo, M.; Moore, C. C., On the regular representation of a nonunimodular locally compact groups, J. Funct. Anal., 21, 209-243 (1976) · Zbl 0317.43013 |
[4] | Khalil, I., Sur l’analyse harmonique du groupe affine de la droite, Stud. Math., 5, 139-167 (1974) · Zbl 0294.43007 |
[5] | Vilenkin, N. Ja., Fonctions spéciales et théorie de la représentation des groupes (1969), Dunod: Dunod Paris · Zbl 0172.18405 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.