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Resolvent at low energy III: The spectral measure

Guillarmou, Colin; Hassell, Andrew; Sikora, Adam


Let M◦ be a complete noncompact manifold and g an asymptotically conic Riemaniann metric on M◦, in the sense that M◦ compactifies to a manifold with boundary M in such a way that g becomes a scattering metric on M. Let Δ be the positive Laplacian associated to g, and P = Δ+ V , where V is a potential function obeying certain conditions. We analyze the asymptotics of the spectral measure dE(λ)=(λ/πi) R(λ + i0) − R(λ − i0) of P+¹/² , where R(λ)=(P − λ²)⁻¹, as λ → 0, in a manner similar...[Show more]

CollectionsANU Research Publications
Date published: 2013-04-02
Type: Journal article
Source: Transactions of the American Mathematical Society
DOI: 10.1090/S0002-9947-2013-05849-7


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