Stability properties for a compactly supported prescale function
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We show that if 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 .
Keywords
Cite
@article{arxiv.math/0110187,
title = {Stability properties for a compactly supported prescale function},
author = {V. Dobric and R. F. Gundy and P. Hitczenko},
journal= {arXiv preprint arXiv:math/0110187},
year = {2007}
}