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Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians

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Abstract

In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ℂn+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.

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Authors and Affiliations

  1. Department of Mathematics, Georgetown University, Washington D.C., 20057, USA

    Der-Chen Chang

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Sai-Kee Yeung

Authors
  1. Der-Chen Chang
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  2. Sai-Kee Yeung
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Correspondence to Der-Chen Chang.

Additional information

Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

The work was supported by National Security Agency, United States Army Research Office and a Hong Kong RGC competitive earmarked research (Grant No. 600607)

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Chang, DC., Yeung, SK. Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians. Sci. China Ser. A-Math. 52, 2570–2589 (2009). https://doi.org/10.1007/s11425-009-0186-4

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  • DOI: https://doi.org/10.1007/s11425-009-0186-4

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