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Renormalized two-body low-energy scattering

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For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d≥3, we introduce a stationary scattering theory for Schrödinger operators which is regular at zero energy. In particular it is well defined at this energy, and we use it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space generalizing parts of [DS1]. Principal tools include global solutions to the eikonal equation and strong radiation condition bounds.
Original languageEnglish
PublisherDepartment of Mathematics, Aarhus University
Number of pages37
Publication statusPublished - 2012
SeriesPreprints
Number3
ISSN1397-4076

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