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Level-Dependent Interpolatory Hermite Subdivision Schemes and Wavelets

  • Mariantonia Cotronei
  • Caroline Moosmüller
  • Tomas SauerEmail author
  • Nada Sissouno
Article

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.

Keywords

Subdivision schemes Hermite schemes Wavelets Coefficient decay 

Mathematics Subject Classification

65T60 65D15 41A58 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Mariantonia Cotronei
    • 1
  • Caroline Moosmüller
    • 2
  • Tomas Sauer
    • 3
    • 4
    Email author
  • Nada Sissouno
    • 5
  1. 1.DIIESUniversità Mediterranea di Reggio CalabriaReggio CalabriaItaly
  2. 2.Department of Chemical and Biomolecular EngineeringJohns Hopkins UniversityBaltimoreUSA
  3. 3.Lehrstuhl für Mathematik mit Schwerpunkt Digitale Signalverarbeitung and FORWISSUniversität PassauPassauGermany
  4. 4.Fraunhofer IIS Research Group on Knowledge Based Image ProcessingPassauGermany
  5. 5.Department of MathematicsTechnical University of MunichGarchingGermany

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