Two-direction multiwavelet moments

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.