Level-dependent interpolatory Hermite subdivision schemes and wavelets

TL;DR

This paper investigates level-dependent Hermite subdivision schemes that preserve polynomial and exponential data, establishing their properties and analyzing the decay of associated multiwavelet coefficients for smooth functions.

Contribution

It introduces a framework for interpolatory level-dependent Hermite subdivision schemes and derives results on the decay of multiwavelet coefficients using a generalized Taylor expansion.

Findings

Multiwavelet coefficients decay for smooth functions.

Interpolatory schemes enable multiresolution analysis.

Polynomial and exponential data are preserved.

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.