Stability properties for a compactly supported prescale function

Details Stability properties for a compactly supported prescale function Stability properties for a compactly supported prescale function

2001-10-17

arxiv.org/abs/math/0110187v1

SIAM J. Math. Anal. 31 (2000), 574-580

Mathematics

Classical Analysis and ODEs

Scientific paper

We show that if $\phi$ is a continuous, minimally supported prescale function, then its translates are linearly independent on any set of positive measure in the unit interval. This generalizes results of Y. Meyer and P. G. Lemarie. This result implies that a stability condition, introduced by Gundy and Kazarian for the study of local convergence of spline wavelet expansions, is satisfied for all expansions arizing from multiresolution analyses generated by such prescale functions $\phi$.

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