Let G be the simplest nilpotent Lie group of step 3. We prove that the densities of the semigroup generated by the sublaplacian on G are not real-analytic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-3,
author = {Jacek Zienkiewicz},
title = {Note on analytic regularity of heat kernels on nilpotent Lie groups},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {163-168},
zbl = {1053.22007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-3}
}
Jacek Zienkiewicz. Note on analytic regularity of heat kernels on nilpotent Lie groups. Colloquium Mathematicae, Tome 96 (2003) pp. 163-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-3/