Aleksi Pyorala

collaborators

5 papers

math.DS2025

On dissonance of self-conformal measures in $R^{d}$

Aleksi PyÃ¶rÃ¤lÃ¤

Let $I^¼$ be a self-conformal measure on $R^{d}$ . In this note we establish conditions for $I^¼$ under which $dim (I^¼ * I^½) = min {d, dim I^¼ + dim I^½}$ holds when $I^½$ …

math.MG2025

Quasisymmetric mappings on two variants of fractal percolation

Roope Anttila, Sylvester Eriksson-Bique, Aleksi PyÃ¶rÃ¤lÃ¤

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 PyÃ¶rÃ¤lÃ¤, 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.CA2025

On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi PyÃ¶rÃ¤lÃ¤

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