Tohoku Mathematical Journal
2012
September
SECOND SERIES VOL. 64, NO. 3

Tohoku Math. J.
64 (2012), 439-451

Title HEAT KERNEL TRANSFORM ON NILMANIFOLDS ASSOCIATED TO H-TYPE GROUPS

Author Aparajita Dasgupta and Sundaram Thangavelu

(Received July 7, 2010, revised January 30, 2012)
Abstract. We study the heat kernel transform on a nilmanifold $ \Gamma \backslash N $ associated to an H-type group. Using a reduction technique we reduce the problem to the case of Heisenberg groups. The image of $ L^2(\Gamma \backslash N) $ under the heat kernel transform is shown to be a direct sum of weighted Bergman spaces.

2000 Mathematics Subject Classification. Primary 22E30; Secondary 35H20, 35K05, 58J35.
Key words and phrases. H-type groups, representations, Laplacians, heat kernels, Weil-Brezin transforms, Bergman spaces.

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