TY - INPR
A1 - Kreitmeier, Wolfgang
T1 - Optimal Quantization for Dyadic Homogeneous Cantor Distributions
N2 - 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.
KW - Maßtheorie
KW - Fraktale Dimension
KW - Iteriertes Funktionensystem
KW - Cantor-Menge
KW - Hausdorff-Dimension
KW - Hausdorff-Maß
KW - Quantization
KW - homogeneous Cantor measures
KW - Quantization dimension
KW - Quantization coefficient
Y1 - 2005
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-3845
N1 - Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de
ER -
TY - INPR
A1 - Kreitmeier, Wolfgang
T1 - Hausdorff measure of uniform self-similar fractals
N2 - Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on Rd. Denote by D the Hausdorff dimension, by HD(E) the Hausdorff measure and by diam (E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and HD = (E) D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover we present a parametrised UIFS where ω depends on c and HD < diam(E)D, if c is small enough.
KW - Maßtheorie
KW - Iteriertes Funktionensystem
KW - Hausdorff-Dimension
KW - Hausdorff-Maß
KW - Self-similar set
KW - Hausdorff measure
Y1 - 2009
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-17948
N1 - This is a preprint of an article accepted for publication in Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version) Copyright (c) by Springer. The original publication is available at www.springerlink.com
ER -