Wave front set for solutions to Schrodinger equations with time-dependent variable coefficients

Abstract

In this paper, we determine the C ∞ -type wave front sets of the solutions to the Schrödinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and estimate the perturb terms of the flat Laplacian on R n , which cannot be estimated by the method in Kato-Ito [6].