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

David Damanik, Anton Gorodetski, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

19 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 languageEnglish
Pages (from-to)1603-1640
Number of pages38
JournalDuke Mathematical Journal
Volume164
Issue number8
DOIs
StatePublished - 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015.

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