Dispersive Estimates of Solutions to the Schrödinger Equation

We prove time decay L1 → L∞ estimates for the Schrödinger group eit(−Δ + V) for real-valued potentials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V \in L^\infty ({\mathbf{R}}^3 )$$\end{document} satisfying V (x) = O (|x|−δ),  |x| ≫ 1, with δ > 5/2.