GEVREY SMOOTHING PROPERTIES OF THE SCHRODINGER EVOLUTION GROUP IN WEIGHTED SOBOLEV SPACES

The Cauchy problem for the Schrodinger Equation i partial derivative u /partial derivative t = -1/2 Delta u + Vu is studied. It is found that for initial data decaying sufficiently rapidly at infinity and Gevrey regular potentials V, the solutions are infinitely differentiable fun ctions of x and t (in fact they are in Gevrey classes). Further, for V = V-1 + V-2, where V-1 satisfies certain smoothness conditions and V- 2 is a rough potential that decays sufficiently rapidly at infinity, t he solutions are still Gevrey regular functions of t. Applications to Scattering Theory are discussed. (C) 1995 Academic Press, Inc.