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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2012, Issue 666


Scattering theory for Schrödinger operators with Bessel-type potentials

S. Albeverio
  • Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, 53115, Bonn, Germany
  • SFB 611, HCM, and IZKS, Bonn, Germany
  • BiBoS, Bielefeld, Germany
  • CERFIM, Locarno, Switzerland
  • Accademia di Architettura, Mendrisio, Switzerland
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  • Other articles by this author:
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/ R. Hryniv
  • Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova st., 79601 Lviv, Ukraine
  • Institute of Mathematics, the University of Rzeszów, 16A Rejtana al., 35-959 Rzeszów, Poland
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/ Ya. Mykytyuk
Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/CRELLE.2011.115


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.

About the article

Published Online: 2011-07-14

Published in Print: 2012-05-01

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: https://doi.org/10.1515/CRELLE.2011.115.

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