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arxiv: math/0308043 · v2 · submitted 2003-08-06 · 🧮 math.AP · math.DG

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

classification 🧮 math.AP math.DG
keywords analyticcontinuationlaplaciannoncompactresolventsymmetrictypeacross
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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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