Harmonic Analysis on Heisenberg Nilmanifolds
نویسنده
چکیده
In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Γ\Hn. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L(Γ\H) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L(Γ\H) in terms of twisted Bergman and Hermite Bergman spaces.
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