Hermite B-Splines: n -Refinability and Mask Factorization

Mariantonia Cotronei and Caroline Moosmüller
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Mariantonia Cotronei: Dipartimento di Ingegneria dell’Informazione, delle Infrastrutture e dell’Energia Sostenibile, Università Mediterranea di Reggio Calabria, Via Graziella Feo di Vito, 89122 Reggio Calabria, Italy
Caroline Moosmüller: Department of Mathematics, University of California, 9500 Gilman Drive, La Jolla, San Diego, CA 92093, USA

Mathematics, 2021, vol. 9, issue 19, 1-11

Abstract: This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets.

Keywords: Hermite splines; polynomial reproduction; subdivision schemes; spectral condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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