2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142022The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on a continuous domain, namely, a real interval. We show that the extended operators replicate the essential properties of their discrete counterparts. More precisely, they form a fully ordered semi-group of four elements, preserve the local trend and the total variation.Classical Analysis and ODEsGeneral Mathematics94A08, 06F05, 26A99text