A Characterization of the Heat Kernel Coefficients

Abstract

We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^{+}$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for the infinite order jet of these coefficients on the diagonal in terms of the local expressions of the powers of the given generalized Laplacian in normal coordinates.

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