HOME > Table of Contents and Abstracts > Vol. 64, No. 3
Tohoku Mathematical Journal
SECOND SERIES VOL. 64, NO. 3
|Tohoku Math. J.|
64 (2012), 439-451
HEAT KERNEL TRANSFORM ON NILMANIFOLDS ASSOCIATED TO H-TYPE GROUPS
Aparajita Dasgupta and Sundaram Thangavelu
(Received July 7, 2010, revised January 30, 2012)
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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