Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique

Faraut, Jacques

Faraut, Jacques

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002), p. 233-241 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

A Gutzmer formula for the complexification of a Riemann symmetric space. We consider a complex manifold $Ω$ and a real Lie group $G$ of holomorphic automorphisms of $Ω$ . The question we study is, for a holomorphic function $f$ on $Ω$ , to evaluate the integral of ${|f|}^{2}$ over a $G$ -orbit by using the harmonic analysis of $G$ . When $Ω$ is an annulus in the complex plane and $G$ the rotation group, it is solved by a classical formula which is sometimes called Gutzmer’s formula. We establish a generalization of it when $Ω$ is a $G$ -invariant domain in the complexification of a Riemannian symmetric space $G / K$ .

Publié le : 2002-12-01

MR 1984103 | Zbl 1116.43006

@article{RLIN_2002_9_13_3-4_233_0,
     author = {Jacques Faraut},
     title = {Formule de Gutzmer pour la complexification d'une espace Riemannien sym\'etrique},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {13},
     year = {2002},
     pages = {233-241},
     zbl = {1116.43006},
     mrnumber = {1984103},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_3-4_233_0}
}

Faraut, Jacques. Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002) pp. 233-241. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_3-4_233_0/

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