Aleksi Pyorala

activity

20202025

collaborators

7 papers

math.DS2025

On dissonance and orthogonal projections of self-conformal measures

Aleksi Pyörälä

Let $μ$ be a self-conformal measure on $R^{d}$ . We establish conditions for $μ$ under which $dim (μ * ν) = min {d, dim μ + dim ν}$ holds when $ν$ is any Ahlfors-regu…

math.MG2025

Quasisymmetric mappings on two variants of fractal percolation

Roope Anttila, Sylvester Eriksson-Bique, Aleksi Pyörälä

We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-exti…

math.CA2025

Furstenberg set theorem for transversal families of functions

Tuomas Orponen, Aleksi Pyörälä, Guangzeng Yi

We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on $L^{p}$ -norms of Fourier t…

math.DS2024

The dimension of projections of planar diagonal self-affine measures

Aleksi Pyörälä

We show that if $μ$ is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption…

math.CA2024

On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi Pyörälä

Let $s \in [0, 1]$ and $t \in [0, min {3 s, s + 1})$ . Let $σ$ be a Borel measure supported on the parabola $P = {(x, x^{2}) : x \in [- 1, 1]}$ satisfying the $s$ -dimensional…

math.DS2023

Scaling limits of self-conformal measures

Balázs Bárány, Antti Käenmäki, Aleksi Pyörälä +1

We show that any self-conformal measure $μ$ on $R$ is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the ne…

math.CA2020

Covering the Sierpiński carpet with tubes

Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala +1

We show that non-trivial $\times N$ -invariant sets in $[0, 1]^{d}$ , such as the Sierpiński carpet and the Sierpiński sponge, are tube-null, that is, they can be covered by a union of…