Refinable functions and positive operators

Authors:
Laura Gori;Francesca Pitolli
Affiliations:
Dip. Me. Mo. Mat. - Università di Roma "La Sapienza", v. A. Scarpa 10, I-00161 Rome, Italy;Dip. Me. Mo. Mat. - Università di Roma "La Sapienza", v. A. Scarpa 10, I-00161 Rome, Italy
Venue:
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Year:
2004

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Abstract

The aim of this paper is to study the shape preserving properties of some positive operators constructed by means of B-bases on a finite interval. These bases are obtained by the integer translates of totally positive compactly supported refinable functions. We shall prove that the constructed B-bases generate, on the interval, multiresolution analyses which reproduce polynomials up to a certain degree.