Hermite B-Splines: n-Refinability and Mask Factorization

Autor: Mariantonia Cotronei, Caroline Moosmüller
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Mathematics, Vol 9, Iss 19, p 2458 (2021)
Druh dokumentu: article
ISSN: 2227-7390
DOI: 10.3390/math9192458
Popis: 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.
Databáze: Directory of Open Access Journals
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