Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type

Details Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type

2003-08-06

arxiv.org/abs/math/0308043v2

Mathematics

Analysis of PDEs

41 pages, 4 figures

Scientific paper

Let $(M,g)$ be a globally symmetric space of noncompact type, of arbitrary
rank, and $\Delta$ its Laplacian. We prove the existence of a meromorphic
continuation of the resolvent $(\Delta-\ev)^{-1}$ across the continuous
spectrum to a Riemann surface multiply covering the plane. The methods are
purely analytic and are adapted from quantum $N$-body scattering.

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