2014/03/29 by E. Skibsted, Erik Skibsted · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems
paper · doi:10.1007/s11854-014-0002-0
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 of the eikonal equation and strong radiation condition bounds.