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arXiv · 1306.4284

Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian

David Damanik·Anton Gorodetski·Boris Solomyak
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Abstract

We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

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David Damanik, Anton Gorodetski, Boris Solomyak. 2014-08-28. Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian. https://doi.org/10.1215/00127094-3119739

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