7 papers
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…
Uniformly perfect measures on strictly convex planar graphs are -flattening
Amir Algom, Tuomas Orponen
Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We…
-Flattening of Self-similar Measures on Non-degenerate Curves
Amir Algom, Osama Khalil
Let be a non-atomic self-similar measure on , and let be its pushforward to a non-degenerate curve in . We show that for every ,…
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…