Semiclassical Estimates for Scattering on the Real Line

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 o...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Authors: Datchev, Kiril, Shapiro, Jacob
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1903.02743