caa a22 4500 445320168 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00023-010-0075-y doi (NATIONALLICENCE)springer-10.1007/s00023-010-0075-y Uniform Convergence of Schrödinger Cocycles over Simple Toeplitz Subshift [Elektronische Daten] [Qing-Hui Liu, Yan-Hui Qu] For locally constant cocycles defined on an aperiodic subshift, Damanik and Lenz (Duke Math J 133(1): 95-123, 2006) proved that if the subshift satisfies a certain condition (B), then the cocycle is uniform. In this paper, we study simple Toeplitz subshifts. We give a criterion that simple Toeplitz subshifts satisfy condition (B), and also give some sufficient conditions that they do not satisfy condition (B). However, we can still prove the uniformity of Schrödinger cocycles over any simple Toeplitz subshift. As a consequence, the related Schrödinger operators have Cantor spectrum of Lebesgue measure 0. We also exhibit a fine structure for the spectrum, and this helps us to prove purely singular continuous spectrum for a large class of simple Toeplitz potentials. Springer Basel AG, 2010 Liu Qing-Hui Department of Computer Science and Engineering, Beijing Institute of Technology, 100081, Beijing, People's Republic of China aut Qu Yan-Hui Department of Mathematics, Tsinghua University, 100084, Beijing, People's Republic of China aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 153-172 1424-0637 12:1<153 2011 12 23 https://doi.org/10.1007/s00023-010-0075-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-010-0075-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Qing-Hui Department of Computer Science and Engineering, Beijing Institute of Technology, 100081, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Qu Yan-Hui Department of Mathematics, Tsinghua University, 100084, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 153-172 1424-0637 12:1<153 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445320168 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer