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

Andras Vasy

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arXiv · 1905.12587

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

Andras Vasy

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Abstract

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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Andras Vasy. 2019-07-13. Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach. https://arxiv.org/abs/1905.12587

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