Resolvents and Martin boundaries of product spaces

Details Resolvents and Martin boundaries of product spaces Resolvents and Martin boundaries of product spaces

2000-12-03

arxiv.org/abs/math/0012009v1

Mathematics

Differential Geometry

38 pages, 5 postscript figures

Scientific paper

In this paper we examine the Laplacian on the product of two asymptotically hyperbolic (or conformally compact, as they are often called) 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 $L^2$ eigenvalues, but it experiences a substantial collapse in the presence of such eigenvalues.

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