Inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential with a virtual level

Abstract

The characteristic properties of scattering data for the Schrodinger operator on the axis with a triangular $2\times 2$ matrix potential are obtained under the simple or multiple virtual levels being possibly present. Under a multiple virtual level, a pole for the reflection coefficient at $k=0$ is possible. For this case, the modified Parseval equality is constructed.

Full Text

Article Information

Title	Inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential with a virtual level
Source	Methods Funct. Anal. Topology, Vol. 15 (2009), no. 4, 301-321
MathSciNet	MR2603831
Copyright	The Author(s) 2009 (CC BY-SA)

Authors Information

F. S. Rofe-Beketov
Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin ave., Kharkiv, 61103, Ukraine

E. I. Zubkova
Ukrainian State Academy of Railway Transport, 7 Feyerbakh square, Kharkiv, 61050, Ukraine 

Citation Example

F. S. Rofe-Beketov and E. I. Zubkova, Inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential with a virtual level, Methods Funct. Anal. Topology 15 (2009), no. 4, 301-321.

BibTex

@article {MFAT536,
    AUTHOR = {Rofe-Beketov, F. S. and Zubkova, E. I.},
     TITLE = {Inverse scattering problem on the axis for the triangular $2\times 2$  matrix potential with a virtual level},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {301-321},
      ISSN = {1029-3531},
  MRNUMBER = {MR2603831},
       URL = {http://mfat.imath.kiev.ua/article/?id=536},
}