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Summer 2010 Linear independence of Parseval wavelets
Marcin Bownik, Darrin Speegle
Illinois J. Math. 54(2): 771-785 (Summer 2010). DOI: 10.1215/ijm/1318598681

Abstract

We establish several results yielding linear independence of the affine system generated by $\psi$ in exchange for conditions on the space $V(\psi)$ of negative dilates. A typical assumption yielding linear independence is that the space $V(\psi)$ is shift-invariant. In particular, the affine system generated by a Parseval wavelet is linearly independent. As an illustration of our techniques, we give an alternative proof of the theorem of Linnell (see Proc. Amer. Math. Soc. 127 (1999), 3269–3277) on linear independence of Gabor systems.

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Marcin Bownik. Darrin Speegle. "Linear independence of Parseval wavelets." Illinois J. Math. 54 (2) 771 - 785, Summer 2010. https://doi.org/10.1215/ijm/1318598681

Information

Published: Summer 2010
First available in Project Euclid: 14 October 2011

zbMATH: 1257.42046
MathSciNet: MR2846482
Digital Object Identifier: 10.1215/ijm/1318598681

Subjects:
Primary: ‎42C40

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 2 • Summer 2010
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