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


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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Correspondence to Der-Chen Chang.

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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 (2009).

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  • sub-Laplacian
  • heat kernel
  • CR-isospectral problem
  • Riemannian zeta function
  • Mellin transform
  • pseudo-hermitian structure


  • Primary: 53C17
  • Secondary: 34K10, 35H20