26 citations · 135 across the 26 of their papers we have counts for
9 papers · 1 filter
Fourier transforms and iterated function systems
Tuomas Sahlsten
We discuss the problem of bounding the Fourier transforms of stationary measures of iterated function systems (IFSs) and how the pseudo-randomness of the IFS either due to arithmet…
On a continuous Sárközy type problem
Borys Kuca, Tuomas Orponen, Tuomas Sahlsten
We prove that there exists a constant with the following property: if is a compact set which contains no pair of the form $\{x, x + (z,…
Trigonometric series and self-similar sets
Jialun Li, Tuomas Sahlsten
Let be a self-similar set on associated to contractions , , for some finite , such that is not a singleto…
Dynamics of the scenery flow and geometry of measures
Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version o…
On Fourier analytic properties of graphs
Jonathan M. Fraser, Tuomas Orponen, Tuomas Sahlsten
We study the Fourier dimensions of graphs of real-valued functions defined on the unit interval [0,1]. Our results imply that the graph of the fractional Brownian motion is almost…
Tangent measures of typical measures
Tuomas Sahlsten
We prove that for a typical Radon measure mu in R^d, every non-zero Radon measure is a tangent measure of mu at mu almost every point. This was already shown by T. O'Neil in his Ph…