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