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Almost Mathieu Operators and Rotation C * ‐Algebras
Author(s) -
Riedel Norbert
Publication year - 1988
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-56.2.281
Subject(s) - mathematics , rotation (mathematics) , pure mathematics , algebra over a field , geometry
A concept of eigenstates is discussed for almost Mathieu operators, relating these operators to the rotation C * ‐algebras they are associated with and to the integrated density of states. For irrational rotations the eigenstates give rise to a notion of multiplicity for all points in the spectrum of an almost Mathieu operator, an integer which is either 1 or 2. It is shown how the occurrence of point spectrum relates to the multiplicity of the corresponding eigenvalues.