Complete asymptotic analysis of low energy scattering for Schrodinger operators with a short-range potential

Abstract

Recent work by Hintz--Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension $d\ge 3$, for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein--Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible.

65 pages, 2 figures; significant expository material added, and a handful of minor typos/mistakes fixed