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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...

Formule de Plancherel pour GL (n, C) / U (p, q).

Nicole Bopp, Pascale Harinck (1992)

Journal für die reine und angewandte Mathematik

Fourier and Poisson transformation associated to a semisimple Symmetrie space.

G. Olafsson (1987)

Inventiones mathematicae

Frame characterizations of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type and their applications.

Yang, Dachun (2002)

Georgian Mathematical Journal

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...

Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups

J. J. Duistermaat, J. A. C. Kolk, V. S. Varadarajan (1983)

Compositio Mathematica

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