Asymptotique à grande energie de la phase de diffusion pour un potentiel

Abstract

About ten years ago several people, Buslaev, Colin de Verdière, Guillopé, and Popov, proved a complete asymptotic expansion, as the energy λ goes to +∞, for the scattering phase s(λ) associated with the Schrödinger operator H=−½Δ+V for compact support, smooth potentials V on Rⁿ. In the present paper, using others techniques, we extend this result to smooth potentials V such that its derivatives of order α are O(|x|^−p−|α|) for some p>n. For V itself this decreasing assumption is more or less optimal.