2000/10/27 by David Borthwick, Borthwick, David · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.DG #math.FA #math.SP
paper · pdf · doi:10.48550/arxiv.math/0010273
AMS-LaTeX, 43 pages, 5 figures
arxiv created 2000/10/27 · arxiv updated 2009/11/30
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 L2 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.