260 citations
- Nanjing UniversityCN9 papers
- Sun Yat-sen UniversityCN6 papers
- Xidian UniversityCN5 papers
- Dalian University of TechnologyCN4 papers
- Inner Mongolia University of Science and TechnologyCN4 papers
- University of BremenDE4 papers
- Zhejiang LabCN4 papers
- Changchun Normal UniversityCN3 papers
- Changzhou UniversityCN3 papers
- National University of Defense TechnologyCN3 papers
- Tsinghua UniversityCN3 papers
- Zhejiang Normal UniversityCN3 papers
4 papers · 1 filter
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…
On the optimal Voronoi partitions for Ahlfors-David measures with respect to the geometric mean error
Sanguo Zhu, Youming Zhou
Let be an Ahlfors-David probability measure on with support . For every , let denote the collection of all the -optimal sets for with…
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…