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

2013/02/14 by Thierry Hargé, Thierry Harge, Harge, Thierry
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1302.3512

arxiv created 2013/02/14 · openalex publication_date 2013/02/14 · arxiv updated 2013/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Borel summation of the small time expansion of the heat kernel. The scalar potential case

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