The propagation property and its application to inverse scattering for the fractional power of the negative Laplacian

Atsuhide Ishida

Published 2016-12-06Version 1

Enss (1983) proved a propagation estimates 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. We study the same type of propagation estimate for the fractional power of the negative Laplacian and, as with the Enss-Weder method, we try to apply our estimate to inverse scattering. We find that the high velocity limit of the scattering operator uniquely determines the short-range interactions.