Revista Matemática Iberoamericana


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Volume 24, Issue 1, 2008, pp. 243–266
DOI: 10.4171/RMI/535

Published online: 2008-04-30

Heat kernel transform for nilmanifolds associated to the Heisenberg group

Bernhard Krötz[1], Sundaram Thangavelu[2] and Yuan Xu[3]

(1) Universität Paderborn, Germany
(2) Indian Institute of Science, Bangalore, India
(3) University of Oregon, Eugene, USA

We study the heat kernel transform on a nilmanifold $M$ of the Heisenberg group. We show that the image of $L^2(M)$ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.

Keywords: Heisenberg group, nilmanifolds, Bergman spaces, heat kernel, Hermite and Laguerre functions

Krötz Bernhard, Thangavelu Sundaram, Xu Yuan: Heat kernel transform for nilmanifolds associated to the Heisenberg group. Rev. Mat. Iberoam. 24 (2008), 243-266. doi: 10.4171/RMI/535