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Semiclassical Estimates for Scattering on the Real Line

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We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used… Click to show full abstract

We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions and in more complicated geometric situations. The novelty in our results lies in the weakness of the assumptions on the potential.

Keywords: scattering real; semiclassical estimates; real line; line; estimates scattering

Journal Title: Communications in Mathematical Physics
Year Published: 2019

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