Gordon-type arguments in the spectral theory of one-dimensional quasicrystals

Details Gordon-type arguments in the spectral theory of one-dimensional quasicrystals Gordon-type arguments in the spectral theory of one-dimensional quasicrystals

1999-12-06

arxiv.org/abs/math-ph/9912005v1

Physics

Mathematical Physics

28 pages

Scientific paper

We review the recent developments in the spectral theory of discrete one-dimensional Schr\"odinger operators with potentials generated by substitutions and circle maps. We discuss how occurrences of local repetitive structures allow for estimates of generalized eigenfunctions. Among the recent applications of this general approach are almost sure and uniform results on the absence of eigenvalues as well as continuity of the spectral measures with respect to Hausdorff measures.

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