An accurate asymptotic estimate for the trace of the heat kernel of a $\Gamma$-pseudo-differential operator

Kazushi Yoshitomi

2025/107/3-4 (10) — DOI: 10.5486/PMD.2025.10201 — pp. 465-476

An accurate asymptotic estimate for the trace of the heat kernel of a $\Gamma$-pseudo-differential operator

Authors: Kazushi Yoshitomi

Abstract:

We study the trace of the heat kernel of an elliptic $\Gamma$-pseudo-differential operator. We obtain an asymptotic formula for it with an optimal error bound. Our work here refines and sharpens a result of Nicola and Rodino, in which its leading asymptotic is obtained.

Keywords: $\Gamma$-pseudo-differential operator, heat kernel, trace

Mathematics Subject Classification: 35S05, 47G30