A. Algom

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20242026

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math.CA2025

Uniformly perfect measures on strictly convex planar graphs are $L^{2}$ -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…

math.CA2025

$L^{2}$ -Flattening of Self-similar Measures on Non-degenerate Curves

Amir Algom, Osama Khalil

Let $I^¼$ be a non-atomic self-similar measure on $R$ , and let $I^½$ be its pushforward to a non-degenerate curve in $R^{d}, d \geq 1$ . We show that for every $I^µ > 0$ ,…

math.DS2025

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…

math.DS2025

Spectral gaps and Fourier decay for self-conformal measures in the plane

Amir Algom, Federico Rodriguez Hertz, Zhiren Wang

Let $I^¦$ be a $C^{I ¨} (C)$ self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the…

Uniformly perfect measures on strictly convex planar graphs are L2-flattening

L2-Flattening of Self-similar Measures on Non-degenerate Curves

Recent progress on pointwise normality of self-similar measures

Spectral gaps and Fourier decay for self-conformal measures in the plane

Uniformly perfect measures on strictly convex planar graphs are $L^{2}$ -flattening

$L^{2}$ -Flattening of Self-similar Measures on Non-degenerate Curves