TY - JOUR
T1 - Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian
AU - Ishida , Atsuhide
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 106
EP - 122
PY - 2020
DA - 2020/01
SN - 10
DO - http://doi.org/10.4208/eajam.050319.110619
UR - https://global-sci.org/intro/article_detail/eajam/13605.html
KW - Scattering theory, inverse problem, fractional Laplacian.
AB - <p style="text-align: justify;">The propagation estimate for the usual free Schrödinger operator established by Enss in 1983, was successfully used by Enss and Weder in inverse scattering in 1995. This approach has been called the Enss-Weder time-dependent method. We derive the same type of estimate but for fractional powers of the negative Laplacian and apply it in inverse scattering. It is found that the high-velocity limit of the scattering operator uniquely determines the short-range interactions.</p>