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Inverse Scattering on the Line with a Transfer Condition

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Abstract

The inverse scattering problem for Sturm–Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In addition, for potentials with compact essential support, we show that the potential can be uniquely reconstructed.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS, Johannesburg, 2050, South Africa

    Sonja Currie & Bruce A. Watson

  2. Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059, Krakow, Poland

    Marlena Nowaczyk

Authors
  1. Sonja Currie
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  2. Marlena Nowaczyk
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  3. Bruce A. Watson
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Corresponding author

Correspondence to Sonja Currie.

Additional information

S. Currie was supported by NRF Grant No. IFR2011040100017. M. Nowaczyk was partially supported by Foundation for Polish Science, Programme Homing 2009/9. B. A. Watson was supported by NRF Grant No. IFR2011032400120.

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Currie, S., Nowaczyk, M. & Watson, B.A. Inverse Scattering on the Line with a Transfer Condition. Mediterr. J. Math. 12, 729–750 (2015). https://doi.org/10.1007/s00009-014-0425-y

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  • DOI: https://doi.org/10.1007/s00009-014-0425-y

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