Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results

We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood the diagonal, generalizing former results obtained particular by Métivier and Ben Arous. The coefficients our are identified terms nilpotentization underlying sub-Riemannian structure. Our approach is purely analytic relies on local global subelliptic estimates as well nature asymptotics kernels. fact that valid not only along diagonal but an main novelty, useful view deriving Weyl laws Laplacians. Incidentally, we number other interesting themselves, such Kac’s principle feeling boundary, singular perturbations operators, smoothing properties selfadjoint semigroups.