Intertwining Operators in Inverse Scattering
In these notes we are going to present some technique which is a multidimensional analogue of some methods which are nowadays standard in scattering theory on the real line for the Schrödinger operator. These methods are based on the construction of operators intertwining the Schrödinger operator with the ‘free operator’ obtained when the potential term is removed. We refer to the monograph  by V. A. Marchenko and to the paper  for a detailed presentation of this technique.
KeywordsFundamental Solution Inverse Scattering Wave Operator Integral Kernel Invertible Element
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- 3.L. Hörmander. The analysis of linear partial differential operators. Springer-Verlag, Berlin, Göttingen, Heidelberg, New York, Tokyo, 1983–1985.Google Scholar
- 4.R. Lagergren. The inverse back-scattering problem (preliminary title). Technical report, Department of mathematics, Växjö University, 2000.Google Scholar
- 5.V.A. Marchenko. Sturm-Liouville operators and applications, volume 22 of Operator theory: Advances and applications. Birkhüser Verlag, Basel-BostonStuttgart, 1986.Google Scholar
- 8.A. Melin. On the general inversion problem. In Brändas, E. and Slander, N., editors, Resonances, volume 325 of Lecture Notes in Physics, pages 47–55. Springer-Verlag, 1989.Google Scholar
- 9.A. Melin. On the use of intertwining operators in inverse scattering. In Holden, H. and Jensen, A., editors, Schrödinger operators, volume 345 of Lecture Notes in Physics, pages 383–400. Springer-Verlag, 1989.Google Scholar
- 10.A. Melin. The inverse scattering problem for a quantum mechanical two-body system. In Gyllenberg, M. and Persson, L.E., editors, Analysis, algebra and computers in mathematical research (proc of 21: s1 Nordic congress of mathematicians), Lecture notes in pure and applied mathematics, pages 247–262. Marcel Dekker, 1994.Google Scholar
- 11.A. Melin. The Faddeev approach to inverse scattering. In Hörmander, L. and Melin, A., editors, Partial differential equations and mathematical physics, Progress in nonlinear differential equations and thir applications, pages 226–245. Birkhäuser, 1996.Google Scholar
- 12.A. Melin. Back-scattering and nonlinear radon transform. Sémin. Equ. Dériv. Partielles, Ecole Polytechnique, pages X IV, 1–14, 1999.Google Scholar
- 13.A. Melin. Intertwining methods in direct and inverse scattering. 2000. monograph in preparation.Google Scholar
- 14.R.G. Newton. Inverse Schrödinger scattering in three dimensions. Texts and monographs in Physics. Springer-Verlag, 1989.Google Scholar