On a regularizing effect of Schrödinger type groups

Abstract

We give estimates for the regularity in the space variables of solutions of Schrödinger type evolution equation with Cauchy Data in L1(Rn). We study the behaviour of these estimates with respect to the time variable, near the origin and at infinity. This is done under the assumption of non degeneracy of the curvature of the wave surfaces. A local decay result is also given. These results are first steps in the study of nonlinear Schrödinger type evolution equations.