Low-frequency dispersive estimates for the Schrödinger group in higher dimensions

Article type: Research Article

Authors: Moulin, Simon | Vodev, Georgi

Affiliations: Université de Nantes, Département de Mathématiques, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44332 Nantes Cedex 03, France. E-mail: {simon.moulin, georgi.vodev}@math.univ-nantes.fr

Abstract: For a large class of real-valued potentials, V(x), x∈Rn, n≥4, we prove dispersive estimates for the low-frequency part of eit(−Δ+V)Pac, provided the zero is neither an eigenvalue nor a resonance of −Δ+V, where Pac is the spectral projection onto the absolutely continuous spectrum of −Δ+V. This class includes potentials V∈L∞(Rn) satisfying V(x)=O(〈x〉−(n+2)/2−ε), ε>0. As a consequence, we extend the results in Commun. Pure Appl. Math. 44 (1991) to a larger class of potentials.

Journal: Asymptotic Analysis, vol. 55, no. 1-2, pp. 49-71, 2007