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

2024/11/06 by Sussman, Ethan
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35C20. Secondary 58J50

paper · doi:10.48550/arxiv.2411.04220

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≥ 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.

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