6 citations · 9 across the 7 of their papers we have counts for
9 papers
One-dimensional Dirichlet forms with prescribed Hölder regularity
Riku Anttila, Roope Anttila
We study a class of strongly local, regular Dirichlet forms on the standard unit interval. The aim of our work is to record some Hölder regularity properties that have not been not…
Badly approximable points on non-linear carpets
Roope Anttila, Jonathan M. Fraser, Henna Koivusalo
The badly approximable points in are those for which Dirichlet's approximation theorem cannot be improved by more than a constant, that is, they are the points most…
Dvoretzky covering problem for general measures
Roope Anttila, Markus Myllyoja
We study the Dvoretzky covering problem for random covering sets driven by general Borel probability measures. As our main result, we solve the problem of covering analytic sets by…
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…
Fibre stability for dominated self-affine sets
Roope Anttila, Alex Rutar
Let be a planar self-affine set. Assuming a weak domination condition on the matrix parts, we prove for all backward Furstenberg directions that $$\max_{E\in\operatorname{T…
Level sets of prevalent Hölder functions
Roope Anttila, Balázs Bárány, Antti Käenmäki
We study the level sets of prevalent Hölder functions. For a prevalent -Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bo…
Multifractal analysis for the pointwise Assouad dimension of self-similar measures
Roope Anttila, Ville Suomala
We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open s…
Slices of the Takagi function
Roope Anttila, Balázs Bárány, Antti Käenmäki
We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp.…
Pointwise Assouad dimension for measures
Roope Anttila
We introduce a pointwise variant of the Assouad dimension for measures on metric spaces, and study its properties in relation to the global Assouad dimension. We show that, in gene…