ANALYTIC SMOOTHING EFFECT FOR SOLUTIONS TO SCHR ¨ ODINGER EQUATIONS WITH NONLINEARITY OF INTEGRAL TYPE 1

We study analytic smoothing effects for solutions to the Cauchy problem for the Schrequation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. The only assumption on the Cauchy data is the weight condition of exponential type and no regularity assump- tion is imposed.