Refinable interpolatory and quasi-interpolatory operators

Authors:
Laura Gori;Francesca Pitolli;Elisabetta Santi
Affiliations:
Dip. Me.Mo.Mat., Universití di Roma "La Sapienza", Via A. Scarpa 10, 00161 Roma, Italy;Dip. Me.Mo.Mat., Universití di Roma "La Sapienza", Via A. Scarpa 10, 00161 Roma, Italy;Dip. Energetica, Universití dell'Aquila, Localitå Monteluco di Roio, 67040 L'Aquila, Italy
Venue:
Mathematics and Computers in Simulation
Year:
2007

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Abstract

In this paper, we present a new class of operators, which are refinable, quasi-interpolatory and satisfy some interpolation conditions. The refinability is achieved by using as functional bases the B-bases corresponding to totally positive refinable functions. We analyze the main properties of the constructed refinable operators and give some convergence results. Some examples are also displayed.