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Connections between the Support and Linear Independence of Refinable Distributions

✍ Scribed by David Ruch; Jianzhong Wang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 226 KB
Volume: 92
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3159

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✦ Synopsis

The purpose of this paper is to study the relationships between the support of a refinable distribution , and the global and local linear independence of the integer translates of ,. It has been shown elsewhere that a compactly supported distribution , has globally independent integer translates if and only if , has minimal convex support. However, such a distribution may have ``holes'' in its support. By insisting that , # L 2 (R) and generates a multiresolution analysis, Lemarie and Malgouyres have ensured that no such holes can occur. In this article we generalize this result to refinable distributions. We also give a result on the local linear independence of the integer translates of ,. We work with integer dilation factor N 2 throughout this paper.

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