Friday, February 22, 2013

1302.5270 (Siegfried Beckus et al.)

Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals    [PDF]

Siegfried Beckus, Felix Pogorzelski
We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. In this context, we characterize the spectrum of these operators by non-uniformity of the transfer matrices and the set where the Lyapunov exponent vanishes. Adapting this result to subshifts satisfying the so-called Boshernitzan condition, it turns out that the spectrum is supported on a Cantor set with Lebesgue measure zero. This generalizes earlier results for Schr\"odinger operators.
View original: http://arxiv.org/abs/1302.5270

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