Heat Kernel Asymptotics for the Generalized Regular Robin Problem

In this chapter we construct the heat Green operator for the generalized regular Robin case (Theorem 24.1) under the conditions (H.0) and (H.3). Moreover, we prove the short time trace formula (24.13) for the heat Green kernel \(e^{-t\,P_{G}}\) with generalized regular Robin condition (Theorem 24.3). This chapter ends with a list of generalized regular Robin heat kernels \(W_{G}(t;a,b)\) and \(V_{G}(t;a,b)\) in Sect. 24.3.