52 citations · 367 across the 81 of their papers we have counts for
5 papers · 1 filter
On the packing measure of self-similar sets
Tuomas Orponen
Building on a recent result of M. Hochman, we give an example of a linear self-similar set K such that 0 < dim K = s < 1 and P^s(K) = 0. This answers a question of Y. Peres and B.…
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…
Non-existence of multi-line Besicovitch sets
Tuomas Orponen
If a compact set K \subset R^2 contains a positive-dimensional family of line-segments in positively many directions, then K has positive measure.
Constancy results for special families of projections
Katrin Fässler, Tuomas Orponen
Let {\mathbb{V} = V x R^l : V \in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing {0} x R^l, and let π_{\mathbb{V}} : R^n --> \mathbb{V} be the orthogonal pr…
On the Packing Dimension and Category of Exceptional Sets of Orthogonal Projections
Tuomas Orponen
We consider several classical results related to the Hausdorff dimension of exceptional sets of orthogonal projections and try to find out whether they have reasonable formulations…