On a class of shape-preserving refinable functions with dilation 3

Authors:
L. Gori;F. Pitolli;E. Santi
Affiliations:
Dip. SBAI, Universití di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy;Dip. SBAI, Universití di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy;Dip. IMEG, Universití dell'Aquila, Via G. Gronchi 18, Zona industriale di Pile, 67100 L'Aquila, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

We analyze the properties of a class of shape-preserving refinable functions with dilation M=3. We give an algorithm to construct totally positive bases with optimal shape-preserving properties on a finite interval. Bernstein-type bases on [0,1] are also treated. Moreover, semiorthogonal wavelets associated with these refinable functions are constructed. Finally, a detailed example is described.