Jump to ContentJump to Main Navigation

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

IMPACT FACTOR increased in 2014: 1.432
Rank 22 out of 310 in category Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 3.585
Source Normalized Impact per Paper (SNIP) 2014: 1.745
Impact per Publication (IPP) 2014: 1.262

Mathematical Citation Quotient (MCQ) 2014: 1.27



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:


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.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Sergio Albeverio, Aleksey Kostenko, Mark Malamud, and Hagen Neidhardt
Journal of Mathematical Physics, 2013, Volume 54, Number 5, Page 052103

Comments (0)

Please log in or register to comment.