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Level-Dependent Interpolatory Hermite Subdivision Schemes and Wavelets

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Abstract

We study many properties of level-dependent Hermite subdivision, focusing on schemes preserving polynomial and exponential data. We specifically consider interpolatory schemes, which give rise to level-dependent multiresolution analyses through a prediction-correction approach. A result on the decay of the associated multiwavelet coefficients, corresponding to a uniformly continuous and differentiable function, is derived. It makes use of the approximation of any such function with a generalized Taylor formula expressed in terms of polynomials and exponentials.

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Acknowledgements

This research was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics.” Most of this research was done while the second author was with the University of Passau. The second author also thanks the Department of Chemical and Biological Engineering, Princeton University, for their hospitality. The fourth author was partially supported by the Emmy Noether Research Group KR 4512/1-1.

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Authors and Affiliations

  1. DIIES, Università Mediterranea di Reggio Calabria, Via Graziella loc. Feo di Vito, 89122, Reggio Calabria, Italy

    Mariantonia Cotronei

  2. Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD, 21218, USA

    Caroline Moosmüller

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

    Tomas Sauer

  4. Fraunhofer IIS Research Group on Knowledge Based Image Processing, Innstr. 43, 94032, Passau, Germany

    Tomas Sauer

  5. Department of Mathematics, Technical University of Munich, Boltzmannstraße 3, 85748, Garching, Germany

    Nada Sissouno

Authors
  1. Mariantonia Cotronei
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  2. Caroline Moosmüller
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  3. Tomas Sauer
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  4. Nada Sissouno
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Corresponding author

Correspondence to Tomas Sauer.

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Communicated by Peter Oswald.

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Cotronei, M., Moosmüller, C., Sauer, T. et al. Level-Dependent Interpolatory Hermite Subdivision Schemes and Wavelets. Constr Approx 50, 341–366 (2019). https://doi.org/10.1007/s00365-018-9444-4

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  • DOI: https://doi.org/10.1007/s00365-018-9444-4

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