# A note on Hermite multiwavelets with polynomial and exponential vanishing moments

## TL;DR

This paper introduces Hermite multiwavelets with polynomial and exponential vanishing moments, featuring level-dependent two-scale relations and filter factorizations, advancing multiresolution analysis for polynomial and exponential data.

## Contribution

It presents a new class of Hermite multiwavelets with combined polynomial and exponential vanishing moments, including their construction and properties.

## Key findings

- Existence of level-dependent two-scale relations.
- Factorization of filter symbols via cancellation operators.
- Construction of biorthogonal multiwavelet systems reproducing polynomial and exponential data.

## Abstract

The aim of the paper is to present Hermite-type multiwavelets satisfying the vanishing moment property with respect to elements in the space spanned by exponentials and polynomials. Such functions satisfy a two-scale relation which is level-dependent as well as the corresponding multiresolution analysis. An important feature of the associated filters is the possibility of factorizing their symbols in terms of the so-called cancellation operator. A family of biorthogonal multiwavelet system possessing the above property and obtained from a Hermite subdivision scheme reproducing polynomial and exponential data is finally introduced.