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Weyl asymptotics for the Laplacian on asymptotically Euclidean spaces. (English) Zbl 0924.58006

Let \(X\) be a smooth compact \(n\)-dimensional manifold with the boundary \(\partial X\) equipped with a scattering metric \(g\). We can define the concept of “asymptotically Euclidean”-ness for \(X\) by determining the behavior of \(g\) near the boundary \(\partial X\).
The purpose of this paper is to obtain the relative trace formula for the Laplacian on the manifold \(X\) which is assumed to be “asymptotically Euclidean”. By using this formula we can obtain the Weyl asymptotics for the scattering phase. Furthermore, we can explicitly compute the leading singularity matrix.
Reviewer: M.Muro (Yanagido)

MSC:

58C40 Spectral theory; eigenvalue problems on manifolds
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