The heat kernel for generalized Heisenberg groups
An explicit expression for the heat kernel \(h_t\) on a generalized Heisenberg or \(H\)-type group \(N\) is obtained. It is shown that \(h_t\) has an analytic extension \(h_z\), \(z\in \mathbb{C}\), \(\text{Re} (z)>0\), and that \(h_z\) is bounded in \(L^p(N)\). Estimates are obtained for \(\| h_z \|_p\), \(1\leq p\leq \infty\).
scientific article; zbMATH DE number 1160137