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

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.