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June 2007 On Refinable Sets
Xin-Rong Dai, Yang Wang
Methods Appl. Anal. 14(2): 165-178 (June 2007).

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.

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Xin-Rong Dai. Yang Wang. "On Refinable Sets." Methods Appl. Anal. 14 (2) 165 - 178, June 2007.

Information

Published: June 2007
First available in Project Euclid: 7 July 2008

zbMATH: 1156.28001
MathSciNet: MR2437101

Subjects:
Primary: 28A78, 28A80

Rights: Copyright © 2007 International Press of Boston

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Vol.14 • No. 2 • June 2007
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