3 papers
math.PR2024
Quantization dimensions of negative order
Marc Kesseböhmer, Aljoscha Niemann
We investigate the possibility of defining meaningful upper and lower quantization dimensions for a compactly supported Borel probability measure of order , including negative v…
math.OC2023
Exact asymptotic order for generalised adaptive approximations
Marc Kesseböhmer, Aljoscha Niemann
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function defined on dyadic cubes.…
math.NT2005
A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
Marc Kesseböhmer, Bernd O. Stratmann
In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We…