2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75560We consider a class of convergence questions for infinite products that arise in wavelet theory when the wavelet filters are more singular than is traditionally built into the assumptions. We establish pointwise convergence properties for the absolute square of the scaling functions. Our proofs are based on probabilistic tools.26 pages, LaTeX2e "elsart" document classClassical Analysis and ODEsFunctional Analysis42C40; 42A16; 43A65; 42A65text