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

作　　者：CHANG Der-Chen YEUNG Sai-Kee 

机构地区：[1]Department of Mathematics,Georgetown University [2]Department of Mathematics,Purdue University

出　　处：《Science China Mathematics》2009年第12期2570-2589,共20页中国科学：数学（英文版）

基　　金：supported by National Security Agency,United States Army Research Offfice and a Hong Kong RGC Competitive Earmarked Research (Grant No. 600607)

摘　　要：In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+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.In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+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.

关 键 词：SUB-LAPLACIAN heat kernel CR-isospectral problem Riemannian zeta function Mellin transform pseudo-hermitian structure Primary: 53C17 Secondary: 34K10  35H20 

分 类 号：O156.4[理学—数学]