Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian
Year: 2020
Author: Atsuhide Ishida
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 106–122
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.050319.110619
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 106–122
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Scattering theory inverse problem fractional Laplacian.
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