Optimal Quantization for Dyadic Homogeneous Cantor Distributions
- For a large class of dyadic homogeneous Cantor distributions in \mathbb{R}, which are not necessarily self-similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non-existence of the quantization coefficient. The class contains all self-similar dyadic Cantor distributions, with contraction factor less than or equal to \frac{1}{3}. For these distributions we calculate the quantization errors explicitly.
Author: | Wolfgang Kreitmeier |
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URN: | urn:nbn:de:bvb:739-opus-3845 |
Document Type: | Preprint |
Language: | English |
Year of Completion: | 2005 |
Date of Publication (online): | 2007/10/31 |
Publishing Institution: | Universität Passau |
Release Date: | 2007/10/31 |
Tag: | Quantization; Quantization coefficient; Quantization dimension; homogeneous Cantor measures |
GND Keyword: | Maßtheorie; Fraktale Dimension; Iteriertes Funktionensystem; Cantor-Menge; Hausdorff-Dimension; Hausdorff-Maß |
Note: | Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de |
Source: | This is a preprint of an article accepted for publication in Mathematische Nachrichten, Print ISSN:0025-584X, Online ISSN:1522-2616, Copyright © by Wiley http://www3.interscience.wiley.com/journal/60500208/home. The digital object identifier (DOI) of the definitive article is 10.1002/mana.200510680. |
Institutes: | Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
MSC-Classification: | 28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx] |
open_access (DINI-Set): | open_access |
Licence (German): | Standardbedingung laut Einverständniserklärung |