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.

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Metadaten
Author:Wolfgang Kreitmeier
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:Cantor-Menge; Fraktale Dimension; Hausdorff-Dimension; Hausdorff-Maß; Iteriertes Funktionensystem; Maßtheorie
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):License LogoStandardbedingung laut Einverständniserklärung

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