1 June 2015 Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian
David Damanik, Anton Gorodetski, Boris Solomyak
Duke Math. J. 164(8): 1603-1640 (1 June 2015). DOI: 10.1215/00127094-3119739

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.

Citation

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David Damanik. Anton Gorodetski. Boris Solomyak. "Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian." Duke Math. J. 164 (8) 1603 - 1640, 1 June 2015. https://doi.org/10.1215/00127094-3119739

Information

Received: 18 June 2013; Revised: 17 July 2014; Published: 1 June 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1358.37117
MathSciNet: MR3352042
Digital Object Identifier: 10.1215/00127094-3119739

Subjects:
Primary: 37D
Secondary: 37C45 , 47B36 , 47N50 , 81Q10

Keywords: convolutions of singular measures , density of states measure , Fibonacci Hamiltonian , hyperbolic measures , Lyapunov exponents , quasicrystals

Rights: Copyright © 2015 Duke University Press

Vol.164 • No. 8 • 1 June 2015
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