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

Article type: Research Article

Authors: Robert, Didier

Affiliations: Centre de Mathematiques, Ecole Poly technique, F–91128 Palaiseau Cedex, France

Note: [] On leave from Departement de Mathematiques, Faculte des Sciences et des Techniques, Universite de Nantes, 44072 Nantes Cedex 03, France.

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.

DOI: 10.3233/ASY-1991-3403

Journal: Asymptotic Analysis, vol. 3, no. 4, pp. 301-320, 1991