A Characterization of the Heat Kernel Coefficients

2001/05/17 by Gregor Weingart, Weingart, Gregor
Computer Science · Engineering · Mathematics · #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Neural Networks and Applications #Radiative Heat Transfer Studies #Spectral Theory (math.SP) #math.DG #math.SP #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0105144

LaTeX2e, 10 pages, no figures, fullpage, Washington cyrillic fonts

arxiv created 2001/05/17 · openalex publication_date 2001/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for t→ 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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