Lulu operators for functions of continuous argument

Abstract

The 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.

Quaestiones Mathematicae 32(2009), 187–202