Analytic smoothing effects for a class of dispersive equations

Abstract

We study the analytic smoothing effect for a class of dispersive equations. In this paper we consider the microlocal analytic smoothness for the solutions of a class of dispersive equations including not only the Schrödinger equation but also the linearized $KdV$ equation. We make use of the Sjöstrand theory of the FBI transform as in Robbiano-Zuily's works in the case of Schrödinger equations.