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math.SP2019★ 14 cited
Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum
Svetlana Jitomirskaya, Simon Becker, Igor Krasovsky
We obtain a representation of the critical almost Mathieu family as a Jacobi matrix that has a singularity. This allows us to prove that the Hausdorff dimension of its spectrum is…
math.SP2002★ 32 cited
Spectral estimates for periodic Jacobi matrices
E. Korotyaev, I. V. Krasovsky
We obtain bounds for the spectrum and for the total width of the spectral gaps for Jacobi matrices on of the form , where $a_…