Propagation property and inverse scattering for fractional powers of negative Laplacian

Atsuhide Ishida, Tokyo University of Science, Japan

Abstract

Enss (1983) proved a propagation estimate for the usual free Schr\"odinger operator that turned out to be very useful for inverse scattering by Enss-Weder (1995). Since then, this method has been called the Enss-Weder time-dependent method. In this talk, first, we introduce the same type propagation estimate for the fractional powers of negative Laplacian. Second, we report about the inverse scattering by applying the Enss-Weder time-dependent method. We find that the high velocity limit of the scattering operator uniquely determines the short-range interactions.