Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

David Damanik; Anton Gorodetski; Boris Solomyak

doi:10.1215/00127094-3119739

Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

David Damanik
, Anton Gorodetski
, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	1603-1640
Number of pages	38
Journal	Duke Mathematical Journal
Volume	164
Issue number	8
DOIs	https://doi.org/10.1215/00127094-3119739
State	Published - 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015.

Funding

Funders	Funder number
National Science Foundation	1067988, 1018433, 0968879

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10.1215/00127094-3119739

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Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

Abstract

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