2001/10/31 by Biswaranjan Behera
Mathematics · #math.FA #msc:42C40
published as Appl. Comp. Harmon. Anal., vol. 13, no. 3, (2002) pp. 277-282. · 8 pages
arxiv created 2002/07/17 · arxiv updated 2009/11/30
The dimension function Dpsi of a band-limited wavelet is bounded by n if the support of its Fourier transform is contained in the interval [-2^(n+2)/3pi, 2^(n+2)/3pi]. For each positive integer n and for each epsilon > 0, we construct a wavelet psi with support of psi contained in [-2^(n+2)/3pi, 2^(n+2)/3pi + epsilon] such that Dpsi > n on a set of positive measure, which proves that [-2^(n+2)/3pi, 2^(n+2)/3pi] is the largest symmetric interval for estimating the dimension function by n.