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math.AP2020
Microlocal approach to the Hausdorff dimension of measures
Rami Ayoush, Michał Wojciechowski
In this paper we study the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. This is achi…
math.CA2020
Hausdorff dimension of measures with arithmetically restricted spectrum
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
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 app…