We compute the heat kernel on the classical and nonisotropic Heisenberg groups, and on the free step two nilpotent groups , by an elementary method, in particular without using Laguerre calculus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9,
author = {Fran\c coise Lust-Piquard},
title = {A simple-minded computation of heat kernels on Heisenberg groups},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {233-249},
zbl = {1052.43013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9}
}
Françoise Lust-Piquard. A simple-minded computation of heat kernels on Heisenberg groups. Colloquium Mathematicae, Tome 96 (2003) pp. 233-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9/