The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator

Details The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator

2008-07-18

arxiv.org/abs/0807.3024v2

Mathematics

Spectral Theory

10 pages; corrected a few typos

Scientific paper

We consider Jacobi matrices with zero diagonal and off-diagonals given by elements of the hull of the Fibonacci sequence and show that the spectrum has zero Lebesgue measure and all spectral measures are purely singular continuous. In addition, if the two hopping parameters are distinct but sufficiently close to each other, we show that the spectrum is a dynamically defined Cantor set, which has a variety of consequences for its local and global fractal dimension.

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