Heat Kernel Asymptotics for the Dirichlet Problem

This chapter is devoted to the study of asymptotic expansions of the compensating operators and terms and heat Green kernels for the Dirichlet case (Theorems 21.7 and 21.8). In the Dirichlet case, we have the short time trace formula (21.34) for the heat Green operator \(e^{-t\,P_{D}}\) with Dirichlet condition (Theorem 21.8). This chapter ends with a list of Dirichlet heat kernels \(W_{D}(t)\) and \(V_{D}(t)\) (see Sect. 21.4).