Geodesic
Hausdorff dimension of measures with arithmetically restricted spectrum
Rami Ayoush1 ; Dmitriy Stolyarov2 ; Michał Wojciechowski1
1 Polish Academy of Sciences, Institute of Mathematics
2 St. Petersburg State University, Department of Mathematics and Computer Science
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 537-551.

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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.
Keywords: Hausdorff dimension, Fourier transform

Rami Ayoush 1 ; Dmitriy Stolyarov 2 ; Michał Wojciechowski 1

1 Polish Academy of Sciences, Institute of Mathematics
2 St. Petersburg State University, Department of Mathematics and Computer Science 
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Rami Ayoush; Dmitriy Stolyarov; Michał Wojciechowski. Hausdorff dimension of measures with arithmetically restricted spectrum. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 537-551. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a31/