LINEAR INDEPENDENCE OF PARSEVAL WAVELETS

摘要

We establish several results yielding linear independence of the affine system generated by ip in exchange for conditions on the space V(ip) of negative dilates. A typical assumption yielding linear independence is that the space V(ip) is shift-invariant. In particular, the affine system generated by a Par-seval 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.