Tohoku Mathematical Journal

Heat kernel transform on nilmanifolds associated to H-type groups

Aparajita Dasgupta and Sundaram Thangavelu

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 3 (2012), 439-451.

Dates
First available in Project Euclid: 11 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1347369372

Digital Object Identifier
doi:10.2748/tmj/1347369372

Mathematical Reviews number (MathSciNet)
MR2979291

Zentralblatt MATH identifier
1260.22007

Subjects
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 35H20: Subelliptic equations 35K05: Heat equation 58J35: Heat and other parabolic equation methods

Keywords
H-type groups representations Laplacians heat kernels Weil-Brezin transforms Bergman spaces

Citation

Dasgupta, Aparajita; Thangavelu, Sundaram. Heat kernel transform on nilmanifolds associated to H-type groups. Tohoku Math. J. (2) 64 (2012), no. 3, 439--451. doi:10.2748/tmj/1347369372. https://projecteuclid.org/euclid.tmj/1347369372


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