Estimation of dimension functions of band-limited wavelets

The dimension function D-psi of a band-limited wavelet psi is bounded by n if its Fourier transform is supported in [-(2(n+2)/3)pi, (2(n+2)/3)pi]. For each n is an element of N and for each epsilon, 0 < epsilon < delta = delta(n), we construct a wavelet psi with supp (psi) over cap subset of or equal to [-(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. This construction also provides a family of (uncountably many) wavelet sets each consisting of infinite number of intervals. (C) 2002 Elsevier Science (USA). All rights reserved.