# On the Inverse Scattering Problem for Jacobi Matrices with the Spectrum on an Interval , a Finite System of Intervals or a Cantor Set of Positive Length

@inproceedings{Yuditskii2002OnTI, title={On the Inverse Scattering Problem for Jacobi Matrices with the Spectrum on an Interval , a Finite System of Intervals or a Cantor Set of Positive Length}, author={P. Yuditskii}, year={2002} }

- Published 2002

Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I + Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the inverse scattering problem. In this article we ask the following natural question — can one find a… CONTINUE READING

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