Note on analytic regularity of heat kernels on nilpotent Lie groups
Colloquium Mathematicum 97 (2003), 163-168 MSC: 22E30, 47D07. DOI: 10.4064/cm97-2-3
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.