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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year


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Scattering theory for Schrödinger operators with Bessel-type potentials

1Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, 53115, Bonn, Germany

2SFB 611, HCM, and IZKS, Bonn, Germany

3BiBoS, Bielefeld, Germany

4CERFIM, Locarno, Switzerland

5Accademia di Architettura, Mendrisio, Switzerland

6Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova st., 79601 Lviv, Ukraine

7Institute of Mathematics, the University of Rzeszów, 16A Rejtana al., 35-959 Rzeszów, Poland

8Lviv National University, 1 Universytetska st., 79602 Lviv, Ukraine

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2012, Issue 666, Pages 83–113, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2011.115, July 2011

Publication History

Published Online:
2011-07-14

Abstract

We show that for the Schrödinger operators on the semi-axis with Bessel-type potentials κ(κ + 1)/x2, , there exists a meaningful direct and inverse scattering theory. Several new phenomena not observed in the “classical case” of Faddeev–Marchenko potentials arise here; in particular, for κ ≠ 0 the scattering function S takes two different values on the positive and negative semi-axes and is thus discontinuous both at the origin and at infinity.

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