Estimation of dimension functions of band-limited wavelets

Abstract

The dimension function D_psi of a band-limited wavelet is bounded by n if the support of its Fourier transform is contained in the interval [-{2^(n+2)/3}pi, {2^(n+2)/3}pi]. For each positive integer n and for each epsilon > 0, we construct a wavelet psi with support of $\hat psi$ contained in [-{2^(n+2)/3}pi, {2^(n+2)/3}pi + epsilon] such that D_psi > n on a set of positive measure, which proves that [-{2^(n+2)/3}pi, {2^(n+2)/3}pi] is the largest symmetric interval for estimating the dimension function by n.