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Fixed points for automorphisms in Cartan domains of type IV

Chiara De Fabritiis (1991)

Rendiconti del Seminario Matematico della Università di Padova

Fonction zêta associée à la série principale sphérique de certains espaces symétriques

Nicole Bopp, Hubert Rubenthaler (1993)

Annales scientifiques de l'École Normale Supérieure

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...

Fractional derivatives of holomorphic functions on bounded symmetric domains of $ℂ^{n}$ .

Lou, Zengjian (1996)

International Journal of Mathematics and Mathematical Sciences

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid Koufany, Bent Ørsted (1996)

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of $SU (2, 2)$ and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside $SU (2, 2)$ . We construct a Cayley transform between the Ol’shanskiĭ semigroup having $U (1, 1)$ as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for $SU (2, 2)$ . This allows calculating the composition series in terms of harmonic analysis on $U (1, 1)$ . In particular we show that the Ol’shanskiĭ Hardy space for $U (1, 1)$ is different...

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