Resolvents and Martin boundaries of product spaces

被引：0

作者：

R. Mazzeo

A. Vasy

机构：

[1] Department of Mathematics,

[2] Stanford University,undefined

[3] Stanford,undefined

[4] CA 94305,undefined

[5] USA,undefined

[6] e-mail: mazzeo@math.stanford.edu,undefined

[7] Department of Mathematics,undefined

[8] Massachusetts Institute of Technology,undefined

[9] MA 02139,undefined

[10] USA,undefined

[11] e-mail: andras@math.mit.edu,undefined

来源：

Geometric & Functional Analysis GAFA | 2002年 / 12卷

关键词：

Asymptotic Behavior; Product Space; Hyperbolic Space; Scattering Theory; Martin Boundary;

D O I：

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中图分类号：

学科分类号：

摘要：

In this paper we examine the Laplacian on the product of two asymptotically hyperbolic spaces from the point of view of geometric scattering theory. In particular, we describe the asymptotic behavior of the resolvent applied to Schwartz functions and that of the resolvent kernel itself. We use these results to find the Martin boundary of the product space. This behaves (nearly) as expected when the factors have no L2 eigenvalues, but it experiences a substantial collapse in the presence of such eigenvalues.

引用

页码：1018 / 1079

页数：61