6 papers · 1 filter
Fourier decay and non-decay for pseudo-affine self-conformal measures
Amir Algom, Snir Ben Ovadia, Federico Rodriguez Hertz +1
We study the sharpness of recent sufficient conditions for polynomial Fourier decay of self conformal measures on the line. First, we construct a iterated function syste…
Smooth projections of self-similar measures
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
We prove a Furstenberg-type criterion for a given orthogonal projection of a self-similar measure to be absolutely continuous, with quantified regularity. It requires exponential m…
How linear can a non-linear hyperbolic IFS be?
Amir Algom, Snir Ben Ovadia, Federico Rodriguez Hertz +1
Motivated by a question of M. Hochman, we construct examples of hyperbolic IFSs on where linear and non-linear behaviour coexist. Namely, for every $2\leq r \leq \inft…
Recent progress on pointwise normality of self-similar measures
Amir Algom
This article is an exposition of recent results and methods on the prevalence of normal numbers in the support of self-similar measures on the line. We also provide an essentially…
Spectral gaps and Fourier decay for self-conformal measures in the plane
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
Let be a self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the…
New results on embeddings of self-similar sets via renormalization
Amir Algom, Michael Hochman, Meng Wu
For self-similar sets , we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conj…