A note on Howe’s oscillator semigroup. (English) Zbl 0674.47029

Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the \(L^ 2({\mathbb{R}}^ n)\) and the Bargmann-Fock realisations by Howe and Brunet-Kramer, respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.
Reviewer: J.Hilgert


47D03 Groups and semigroups of linear operators
47B38 Linear operators on function spaces (general)
Full Text: DOI Numdam EuDML


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