Positive operators based on scaling functions

In this paper we consider linear operators of Bernstein–Schoenberg type, constructed on B-bases, generated from a finite system of integer shifts of a scaling function (or refinable function), belonging to a large class of totally positive scaling functions introduced in [9]. These operators where introduced in [12], where their $L^2$ approximation properties were discussed. Here we examine their spectral properties and best least square approximations.