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A note on Howe's oscillator semigroup

Joachim Hilgert — 1989

Annales de l'institut Fourier

Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the L 2 ( n ) and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

Spherical functions on ordered symmetric spaces

Jacques FarautJoachim HilgertGestur Ólafsson — 1994

Annales de l'institut Fourier

We define on an ordered semi simple symmetric space = G / H a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when G is a complex group, H a real form of G , and when ...

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