4 papers
Two-scale branching functions and inhomogeneous attractors
Vilma Orgoványi, Alex Rutar
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectru…
A fractal local smoothing problem for the wave equation
David Beltran, Joris Roos, Alex Rutar +1
For any given set , we discuss a fractal frequency-localized version of the local smoothing estimates for the half-wave propagator with times in . A conjec…
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…
On the uniformity and size of microsets
Richárd Balka, Vilma Orgoványi, Alex Rutar
We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set with Assouad dimen…