Hausdorff dimension of measures with arithmetically restricted spectrum

Authors

  • Rami Ayoush Polish Academy of Sciences, Institute of Mathematics
  • Dmitriy Stolyarov St. Petersburg State University, Department of Mathematics and Computer Science
  • Michał Wojciechowski Polish Academy of Sciences, Institute of Mathematics

Keywords:

Hausdorff dimension, Fourier transform

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 those bounds via adaptation of our previous results for martingales on \(q\)-regular trees to a specific backwards martingale. To show the sharpness of our method, we improve the best numerical lower bound known for the Hausdorff dimension of certain Riesz products.
Issue
Vol. 46 No. 1 (2021)
Section
Articles

Published

2021-06-21

How to Cite

Ayoush, R., Stolyarov, D., & Wojciechowski, M. (2021). Hausdorff dimension of measures with arithmetically restricted spectrum. Annales Fennici Mathematici, 46(1), 537–551. Retrieved from https://afm.journal.fi/article/view/109627

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