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Level-dependent interpolatory hermite subdivision schemes and wavelets

: Cotronei, M.; Moosmüller, C.; Sauer, T.; Sissouno, N.


Constructive approximation 50 (2019), No.2, pp.341-366
ISSN: 0176-4276 (Print)
ISSN: 1432-0940 (Online)
Journal Article
Fraunhofer IIS ()

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.