Multiresolution analyses originated from nonstationary subdivision schemes

Authors:
Laura Gori;Francesca Pitolli
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
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 6
Cited 1

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Totally positive functions through nonstationary subdivision schemes

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Technical Section: Multiresolutions numerically from subdivisions

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Abstract

We analyze the properties of a new class of totally positive refinable functions obtained from nonstationary subdivision schemes. We show that the corresponding system of the integer translates is linearly independent, satisfies a Whitney-Schoenberg condition, reproduces polynomials up to a certain degree and generates a multiresolution analysis. Finally, pre-wavelets and bases on the interval are constructed.