Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach

Andras Vasy

Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach

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arxiv 1905.12587 v2 pith:NHNCMDKW submitted 2019-05-29 math.AP math.DG

Andras Vasy This is my paper · ORCID

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keywords lagrangianscatteringspacesabsorptionasymptoticallyconicgeneralizationslimiting

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We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces which encode the Lagrangian regularity of generalizations of `outgoing spherical waves' of scattering theory, and indeed this persists in the `physical half plane'.

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Existence and asymptotics of nonlinear Helmholtz eigenfunctions
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Small nonlinear Helmholtz equations have solutions with prescribed incoming and outgoing wave patterns at infinity, on Euclidean space and asymptotically conic manifolds, under a dimension-degree condition.

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