naa a22 4500 510781675 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11854-013-0014-1 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0014-1 Spectral properties of a limit-periodic Schrödinger operator in dimension two [Elektronische Daten] [Yulia Karpeshina, Young-Ran Lee] We study the Schrödinger operator H = −Δ + V(x) in dimension two, V(x) being a limit-periodic potential. We prove that the spectrum of H contains a semiaxis, and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves exp( $$i\left\langle {\overrightarrow k ,\overrightarrow x } \right\rangle $$ ) at the high energy region. Second, the isoenergetic curves in the space of momenta $$\overrightarrow k $$ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous. Hebrew University Magnes Press, 2013 Karpeshina Yulia Department of Mathematics, University of Alabama at Birmingham, 1300 University Boulevard, 35294, Birmingham, AL, USA aut Lee Young-Ran Department of Mathematics, Sogang University, Shinsu-Dong 1, Mapo-Gu, 121-742, Seoul, South Korea aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 1-84 0021-7670 120:1<1 2013 120 11854 https://doi.org/10.1007/s11854-013-0014-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0014-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karpeshina Yulia Department of Mathematics, University of Alabama at Birmingham, 1300 University Boulevard, 35294, Birmingham, AL, USA aut NATIONALLICENCE 700 1- Lee Young-Ran Department of Mathematics, Sogang University, Shinsu-Dong 1, Mapo-Gu, 121-742, Seoul, South Korea aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 120/1(2013-08-01), 1-84 0021-7670 120:1<1 2013 120 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer