Illinois Journal of Mathematics

Linear independence of Parseval wavelets

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.

Article information

Source
Illinois J. Math., Volume 54, Number 2 (2010), 771-785.

Dates
First available in Project Euclid: 14 October 2011

https://projecteuclid.org/euclid.ijm/1318598681

Digital Object Identifier
doi:10.1215/ijm/1318598681

Mathematical Reviews number (MathSciNet)
MR2846482

Zentralblatt MATH identifier
1257.42046

Subjects
Primary: 42C40: Wavelets and other special systems

Citation

Bownik, Marcin; Speegle, Darrin. Linear independence of Parseval wavelets. Illinois J. Math. 54 (2010), no. 2, 771--785. doi:10.1215/ijm/1318598681. https://projecteuclid.org/euclid.ijm/1318598681

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