Physics – Mathematical Physics
Scientific paper
2005-11-04
Physics
Mathematical Physics
33 pages; a preliminary version
Scientific paper
An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. 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 (Schr\"odinger) operator.
Kupin Stanislav
Peherstorfer Franz
Volberg Alexander
Yuditskii Peter
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