Abstract
An original approach to the inverse scattering for Jacobi matrices was recently suggested in [20]. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schrödinger) operator.
Partially supported by NSF grant DMS-0501067 the Austrian Founds FWF, project number: P 16390-N04 and Marie Curie International Fellowship within the 6th European Community Framework Programme, Contract MIF1-CT-2005-006966.
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Kupin, S., Peherstorfer, F., Volberg, A., Yuditskii, P. (2008). Inverse Scattering Problem for a Special Class of Canonical Systems and Non-linear Fourier Integral. Part I: Asymptotics of Eigenfunctions. In: Janas, J., Kurasov, P., Naboko, S., Laptev, A., Stolz, G. (eds) Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, vol 186. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8755-6_15
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