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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: . Volume 2012, Issue 666, Pages 83–113, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2011.115, May 2012
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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