Hausdorff dimension of measures with arithmetically restricted spectrum
Classical Analysis and ODEs
2020-02-18 v1
Abstract
We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via application of a general result for abstract -regular martingales to the Gundy--Varopoulos backwards martingale. To show the sharpness of our method, we improve the best known numerical lower bound for the Hausdorff dimension of certain Riesz products.
Cite
@article{arxiv.2002.06443,
title = {Hausdorff dimension of measures with arithmetically restricted spectrum},
author = {Rami Ayoush and Dmitriy Stolyarov and Michał Wojciechowski},
journal= {arXiv preprint arXiv:2002.06443},
year = {2020}
}