R. Balka

activity

20212025

collaborators

3 papers

math.CA2025

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 $(a_{n})$ tends to zero in $\ma…

math.MG2024

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 $K \subset R^{d}$ with Assouad dimen…

math.CA2021

The range of dimensions of microsets

Richárd Balka, Márton Elekes, Viktor Kiss

We say that $E$ is a microset of the compact set $K \subset R^{d}$ if there exist sequences $λ_{n} \geq 1$ and $u_{n} \in R^{d}$ such that $(λ_{n} K + u_{n}) \cap [0, 1]^{d}$ conv…