Volume 10, Issue 1
Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian

Atsuhide Ishida

10.4208/eajam.050319.110619

East Asian J. Appl. Math., 10 (2020), pp. 106-122.

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  • 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.

  • History

Published online: 2020-01

  • AMS Subject Headings

81Q10, 81U05, 81U40

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