Some remarks on the complex heat kernel in the scalar potential case

Thierry Harge (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

In previous works, we used a so-called deformation formula in order to study, in particular, the Borel summability of the heat kernel of some operators. A goal of this paper is to collect miscellaneous remarks related to these works. Here the complex setting plays an important role. Moreover, the deformation formula provides a solution of the heat equation in ''unusual'' cases. We also give a uniqueness statement concerning these cases.

Mots clés: heat kernel; asymptotic expansion; Wigner-Kirkwood expansion; complex variables; Borel summation

Domaines: Physique mathématique [math-ph]

Thierry Harge. Some remarks on the complex heat kernel in the scalar potential case. 2013. ⟨hal-00788563⟩