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

الأصل · EN

Let (M,g) be a globally symmetric space of noncompact type, of arbitrary rank, and Δ its Laplacian. We prove the existence of a meromorphic continuation of the resolvent (Δ-)⁻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.