Asymptotic and exact expansions of heat traces

Abstract

We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.

44 LaTeX pages, 2 figures

References in corpus (4)

• Heat kernel and number theory on NC-torus
• The spectral action and cosmic topology
• Heat Trace Asymptotics on Noncommutative Spaces
• Heat trace and spectral action on the standard Podles sphere

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