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Renormalized two-body low-energy scattering

By E. Skibsted
No. 03, March 2012
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, 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.
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