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Hermite B-Splines: n -Refinability and Mask Factorization

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mariantonia Cotronei & Caroline Moosmüller, 2021. "Hermite B-Splines: n -Refinability and Mask Factorization," Mathematics, MDPI, vol. 9(19), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2458-:d:649008
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