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Asymptotic and Exact Expansions of Heat Traces

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  • Published: 20 October 2015
  • Volume 18, article number 28, (2015)
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Asymptotic and Exact Expansions of Heat Traces
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  • Michał Eckstein1 &
  • Artur Zając2 

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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.

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Authors and Affiliations

  1. Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 11, 30–348, Kraków, Poland

    Michał Eckstein

  2. Faculty of Mathematics and Computer Science, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 6, 30–348, Kraków, Poland

    Artur Zając

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  1. Michał Eckstein
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Correspondence to Michał Eckstein.

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Eckstein, M., Zając, A. Asymptotic and Exact Expansions of Heat Traces. Math Phys Anal Geom 18, 28 (2015). https://doi.org/10.1007/s11040-015-9197-2

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  • Received: 16 March 2015

  • Accepted: 08 September 2015

  • Published: 20 October 2015

  • DOI: https://doi.org/10.1007/s11040-015-9197-2

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Keywords

  • Heat traces
  • Asymptotic expansions
  • Spectral theory
  • Zeta-functions
  • General Dirichlet series

Mathematics Subject Classification (2010)

  • Primary: 11M36
  • Secondary: 30B50
  • 35K08
  • 41A60
  • 47B15
  • 81Q10
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