Absolute continuity of Bernoulli convolutions for algebraic parameters
Classical Analysis and ODEs
2019-04-02 v4 Combinatorics
Dynamical Systems
Abstract
We prove that Bernoulli convolutions are absolutely continuous provided the parameter lambda is an algebraic number sufficiently close to 1 depending on the Mahler measure of lambda.
Cite
@article{arxiv.1602.00261,
title = {Absolute continuity of Bernoulli convolutions for algebraic parameters},
author = {Péter P. Varjú},
journal= {arXiv preprint arXiv:1602.00261},
year = {2019}
}
Comments
58 pages; version accepted for publication in J. Amer. Math. Soc.; minor corrections based on referees' reports; results and proofs are not changed