Methods and Applications of Analysis

On Refinable Sets

Xin-Rong Dai and Yang Wang

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Abstract

A refinable set is a compact set with positive Lebesgue measure whose characteristic function satisfies a refinement equation. Refinable sets are a generalization of self-affine tiles. But unlike the latter, the refinement equations defining refinable sets may have negative coefficients, and a refinable set may not tile. In this paper, we establish some fundamental properties of these sets.

Article information

Source
Methods Appl. Anal., Volume 14, Number 2 (2007), 165-178.

Dates
First available in Project Euclid: 7 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.maa/1215442821

Mathematical Reviews number (MathSciNet)
MR2437101

Zentralblatt MATH identifier
1156.28001

Subjects
Primary: 28A78: Hausdorff and packing measures 28A80: Fractals [See also 37Fxx]

Keywords
Hausdorff dimension self-similar set finite type condition

Citation

Dai, Xin-Rong; Wang, Yang. On Refinable Sets. Methods Appl. Anal. 14 (2007), no. 2, 165--178. https://projecteuclid.org/euclid.maa/1215442821


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