Journal
GEOMETRIC AND FUNCTIONAL ANALYSIS
Volume 12, Issue 5, Pages 1018-1079Publisher
BIRKHAUSER VERLAG AG
DOI: 10.1007/PL00012647
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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 L-2 eigenvalues, but it experiences a substantial collapse in the presence of such eigenvalues.
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