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Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator刘跟前教授, 北京理工大学报告时间:2015年5月12日(星期二),下午14:00—16:00报告地点:北航数学与系统科学ag平台app下载主 213学术交流厅报告摘要:

For a given bounded domain [1]with smooth boundary in a smooth Riemannian manifold (M, g), by decomposing the Dirichlet-to-Neumann operator into a sum of the square root of the Laplacian and a pseudodifferentialoperator, and by applying Grubb's method of symbolic calculus for the correspond-ing pseudodifferential heat kernel operators, we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to Dirichlet-to-Neumann operator as t→0+. In particular, we explicitly give the first four coefficients of this asymptotic expansion. These coef-ficients give precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the Steklov problem.

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