R. Hatamleh, V. A. Zolotarev, “On the abstract inverse scattering problem for trace class perturbations”, Zh. Mat. Fiz. Anal. Geom., 2017, Volume 13, Number 1,Pages <nobr>3

On the abstract inverse scattering problem for trace class perturbations

R. Hatamleh^a, V. A. Zolotarev^b

^a Department of Mathematics, Jadara University, Irbid-Jordan
^b B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv 61103, Ukraine

Abstract: The scattering problem for a pair of selfadjoint operators $\{L_0, L\}$, where $L - L_0$ 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.

Key words and phrases: scattering matrix, Friedrichs–Faddeev model, inverse scattering problem.

MSC: 47A45

Received: 15.07.2015
Revised: 03.11.2015

Language: English

DOI: 10.15407/mag13.01.003