Analytic continuation of the resolvent of the Laplacian on SL(3)/SO(3)

Details Analytic continuation of the resolvent of the Laplacian on SL(3)/SO(3) Analytic continuation of the resolvent of the Laplacian on SL(3)/SO(3)

2002-08-14

arxiv.org/abs/math/0208116v2

Mathematics

Analysis of PDEs

20 pages, 2 figures

Scientific paper

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work we described the resolvent, and specifically the asymptotic behavior of the Green's function, on SL(3)/SO(3) using methods from three-particle scattering. Here we extend the technique of complex scaling to symmetric spaces to show that the resolvent continues analytically across the spectrum.

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