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

Jacques Faraut (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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...

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