The heat kernel for $H$-type groups
Jennifer Randall · Project Euclid (Cornell University) · 1992
Theorem 1 gives an explicit formula for the heat kernel on an H -type group. Folland (2] has shown that for stratified nilpotent Lie groups the heat semigroup is a semigroup of kernel operators on LP, 1 5 p < oo and on Co. Cygan (1] has obtained formulas for heat kernels for any two step nilpotent simply connected Lie group. Cygan found the heat kernel for a free simply connected two step nilpotent group, G, using the representation of L1 (G) obtained from the irreducible unitary representation of G in a Hilbert space. He then obtained the heat kernel for a general two step nilpotent Lie group by the method of descent.