**Shouzhi Yang**

## Extension of Multiresolution Analysis and
the Construction of Orthogonal Multiwavelets

**Abstract:**

A procedure of the extension of orthogonal multiresolution analysis is
introduced by assuming that $\phi_1(x)$ ia an orthogonal uniscaling function and
constructing a new orthogonal multiscaling function $\Phi(x)=\linebreak {}
[\phi_1(x),\phi_{2}(x)]^T$\!. Moreover, an explicit formula of the orthogonal
multiwavelets associated with $\Phi(x)$ is obtained. Finally, a construction
example is given.

**Keywords:**

Extension of MRA, orthogonal scaling function, orthogonal multiscaling
functions, orthogonal multiwavelets.

**MSC 2000:** 42C40, 65T60