2-nd International Conference OFEA'2001 "Optimization of Finite Element Approximation and Splines and Wavelets", June 25-29, 2001, St.-Petersburg

Positive operators based on scaling functions

L. Gori^a, F. Pitolli^a, E. Santi<sup>b

a</sup> Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, University of Rome "La Sapienza"
^b Department of Engineering for Mechanics, Energy and Management, University of L'Aquila

Abstract: 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.

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