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Factorization of Hermite subdivision operators preserving exponentials and polynomials

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Abstract

In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and associated consecutive derivatives. We are mainly interested in studying the exponential and polynomial preservation capability of such kind of operators, which can be expressed in terms of a generalization of the spectral condition property in the spaces generated by polynomials and exponential functions. The main tool for our investigation are convolution operators that annihilate the aforementioned spaces, which apparently is a general concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of the subdivision operator.

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Authors and Affiliations

  1. DIEF, Università di Firenze, Viale Morgagni 40/44, 50134, Firenze, Italy

    Costanza Conti

  2. DIIES, Università Mediterranea di Reggio Calabria, Via Graziella, 89122, Reggio Calabria, Italy

    Mariantonia Cotronei

  3. Lehrstuhl für Mathematik mit Schwerpunkt Digitale Signalverarbeitung, Universität Passau, Innstr. 43, 94032, Passau, Germany

    Tomas Sauer

Authors
  1. Costanza Conti
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  2. Mariantonia Cotronei
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  3. Tomas Sauer
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Correspondence to Costanza Conti.

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Communicated by: T. Lyche

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Conti, C., Cotronei, M. & Sauer, T. Factorization of Hermite subdivision operators preserving exponentials and polynomials. Adv Comput Math 42, 1055–1079 (2016). https://doi.org/10.1007/s10444-016-9453-4

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  • DOI: https://doi.org/10.1007/s10444-016-9453-4

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