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/