We study the heat kernel transform on a nilmanifold of the Heisenberg group. We show that the image of under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.
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Bernhard Krötz, Sundaram Thangavelu, Yuan Xu, Heat kernel transform for nilmanifolds associated to the Heisenberg group. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 243–266DOI 10.4171/RMI/535