16 citations · 47 across the 4 of their papers we have counts for
4 papers
Quantization dimensions of compactly supported probability measures via Rényi dimensions
Marc Kesseböhmer, Aljoscha Niemann, Sanguo Zhu
We provide a complete picture of the upper quantization dimension in terms of the Rényi dimension by proving that the upper quantization dimension of order f…
Some recent developments in quantization of fractal measures
Marc Kesseböhmer, Sanguo Zhu
We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of…
The quantization for Markov-type measures on a class of ratio-specified graph directed fractals
Marc Kesseböhmer, Sanguo Zhu
We study the asymptotic quantization error of order for Markov-type measures on a class of ratio-specified graph directed fractals. We show that the quantization dimension…
On the quantization for self-affine measures on Bedford-McMullen carpets
Marc Kesseböhmer, Sanguo Zhu
For a self-affine measure on a Bedford-McMullen carpet we prove that its quantization dimension exists and determine its exact value. Further, we give various sufficient conditions…