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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 36, Pages 2277-2301
http://dx.doi.org/10.1155/S0161171203206268

The spectrum of a class of almost periodic operators

Department of Mathematics, Tulane University, New Orleans 70118, LA, USA

Received 19 June 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For almost Mathieu operators, it is shown that the occurrence of Cantor spectrum and the existence, for every point in the spectrum and suitable phase parameters, of at least one localized eigenfunction which decays exponentially are inconsistent properties.