Scattering theory for conformally compact metrics with variable curvature at infinity

Details Scattering theory for conformally compact metrics with variable curvature at infinity Scattering theory for conformally compact metrics with variable curvature at infinity

2000-10-27

arxiv.org/abs/math/0010273v1

Mathematics

Spectral Theory

AMS-LaTeX, 43 pages, 5 figures

Scientific paper

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix is shown to be a pseudodifferential operator. For generic frequency in this part of the continuous spectrum, we give an explicit construction of the resolvent kernel.

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