Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure
- For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error.
| Author: | Wolfgang Kreitmeier |
|---|---|
| URN: | urn:nbn:de:bvb:739-opus-7374 |
| Document Type: | Preprint |
| Language: | English |
| Year of Completion: | 2007 |
| Date of Publication (online): | 2008/01/02 |
| Publishing Institution: | Universität Passau |
| Release Date: | 2008/01/02 |
| Tag: | Euler characteristic; Euler exponent; Hausdorff dimension; Homogeneous Cantor set; quantization coefficient; quantization dimension |
| 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 Journal of Mathematical Analysis and Applications, ISSN: 0022-247X. Copyright (c) by Elsevier. URL: http://www.elsevier.com/. The digital object identifier (DOI) of the definitive article is 10.1016/j.jmaa.2007.12.052 |
| 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 / 28A78 Hausdorff and packing measures |
| 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 |
