Algorithms for the calculation of the heat kernel coefficients

TL;DR

This paper reviews various methods for calculating the local asymptotic expansion of the heat kernel associated with Laplace-type operators, highlighting historical approaches developed by the authors.

Contribution

It provides a comparative overview of multiple approaches for heat kernel coefficient calculation, emphasizing methods previously developed by the authors.

Findings

Different methods for heat kernel coefficient calculation are summarized.

The paper highlights the historical development of these approaches.

It clarifies the applicability of each method to Laplace-type operators.

Abstract

We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in more detail.