Propagation Property and Inverse Scattering for Fractional Powers of the Negative Laplacian

Abstract

Enss (1983) proved a propagation estimate for the usual free Schrödinger 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, the speaker will introduce the same type propagation estimate for the fractional powers of negative Laplacian. Second, he will report about the inverse scattering by applying the Enss-Weder time-dependent method. He and his group find that the high velocity limit of the scattering operator uniquely determines the short-range interactions.

About the speaker

Prof. Atsuhide Ishida received his PhD at Kobe University. He joined the Tokyo University of Science in 2016 and is currently a Junior Associate Professor at the Department of Liberal Arts in the Faculty of Engineering there.

Prof. Ishida’s research focuses on partial differential equation and functional analysis. He received the Young Scholar Award in the 3rd East Asia Section of Inverse Problems International Association - Young Scholars Symposium in 2018.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.