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

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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-3119739

Cite this

@article{2a60e81a243042eeb83d227df221e59b,

title = "Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian",

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.",

author = "David Damanik and Anton Gorodetski and Boris Solomyak",

note = "Publisher Copyright: {\textcopyright} 2015.",

year = "2015",

doi = "10.1215/00127094-3119739",

language = "الإنجليزيّة",

volume = "164",

pages = "1603--1640",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "8",

}

TY - JOUR

T1 - Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

AU - Damanik, David

AU - Gorodetski, Anton

AU - Solomyak, Boris

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84930852496&partnerID=8YFLogxK

U2 - 10.1215/00127094-3119739

DO - 10.1215/00127094-3119739

M3 - مقالة

SN - 0012-7094

VL - 164

SP - 1603

EP - 1640

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 8

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this