Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 1, pp. 3-34   https://doi.org/10.15407/mag13.01.003     ( to contents , go back )
https://doi.org/10.15407/mag13.01.003

On the Abstract Inverse Scattering Problem for Trace Class Perturbations

R. Hatamleh

Department of Mathematics, Jadara University, Irbid-Jordan
E-mail: raedhat@yahoo.com

V.A. Zolotarev

B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine
E-mail: vazolotarev@gmail.com

Received July 15, 2015, revised November 3, 2015

Abstract

The scattering problem for a pair of selfadjoint operators {L0, L}, where L - L0 is of trace-class, is studied. The explicit form of the scattering matrix and its properties are defined. The equation for the inverse problem is obtained.

Mathematics Subject Classification 2000: 47A45.
Key words: scattering matrix, Friedrichs-Faddeev model, inverse scattering problem.

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