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

Atsuhide Ishida

DOI: 10.4208/eajam.050319.110619

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

Published online: 2020-01

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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.

  • Keywords

Scattering theory, inverse problem, fractional Laplacian.

  • AMS Subject Headings

81Q10, 81U05, 81U40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

aishida@rs.tus.ac.jp (Atsuhide Ishida)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-106, author = {Ishida , Atsuhide}, title = {Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.050319.110619}, url = {http://global-sci.org/intro/article_detail/eajam/13605.html} }
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 -

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.

Ishida , Atsuhide. (2020). Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian. East Asian Journal on Applied Mathematics. 10 (1). 106-122. doi:10.4208/eajam.050319.110619
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