Linear Independence of Parseval Wavelets
نویسندگان
چکیده
We establish several results yielding linear independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding linear independence is that the space V (ψ) 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 [14] on linear independence of Gabor systems.
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