4 papers
New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions
Richárd Balka, Tamás Keleti
We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that…
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…
Effective eigenvalue approximation from moments for self-adjoint trace-class operators
Richárd Balka, Gábor Homa, András Csordás
Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator we define a set $Î…
Signed null sequences and Hausdorff dimension
Richárd Balka, Kornélia Héra, Gergely Kiss
We investigate the convergence of signed null sequences of the form \[ \sum_{n=1}^\infty \varepsilon_n a_n, \quad \varepsilon_n \in \{-1,1\}, \] where tends to zero in $\ma…