Two-direction multiwavelet moments

TL;DR

This paper introduces two methods for computing continuous moments of orthogonal two-direction multiscaling functions and multiwavelets, enhancing the flexibility and generality over traditional one-direction approaches.

Contribution

It proposes two novel methods, doubling and separation, for calculating continuous moments of two-direction multiscaling functions and multiwavelets, with illustrative examples.

Findings

Two methods successfully compute continuous moments.

Methods improve flexibility over one-direction multiscaling functions.

Examples demonstrate practical application of the methods.

Abstract

Two-direction multiscaling functions $\boldphi$ and two-direction multiwavelets $\boldpsi$ associated with $\boldphi$ are a more general and more flexible setting than one-direction multiscaling functions and multiwavelets. In this paper, we derive two methods for computing continuous moments of orthogonal two-direction multiscaling functions $\boldphi$ and orthogonal two-direction multiwavelets $\boldpsi$ associated with $\boldphi$. The first method is by doubling and the second method is by separation. Two examples for both methods are given.