A note on Hermite multiwavelets with polynomial and exponential vanishing moments
This provides a theoretical framework for multiwavelet design with combined polynomial and exponential vanishing moments, relevant for signal processing and numerical analysis.
The paper constructs Hermite-type multiwavelets with vanishing moments for both polynomials and exponentials, enabling level-dependent two-scale relations and factorization via cancellation operators. A family of biorthogonal multiwavelet systems derived from Hermite subdivision schemes is introduced.
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.