Bulletin of the
Korean Mathematical Society BKMS

In this paper, we derive a characterization of orthonormal balanced multiwavelets of order $p$ in terms of the continuous moments of the multiscaling function $\boldsymbol \phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order $p$ (or degree $p-1$) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree $p-1$ in terms of continuous moments for orthonormal balanced multiwavelets of order $p$. Balancing of order $p$ implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree $p-1$. We derive an algorithm for computing the polynomial of degree $p-1$.

Keywords: multiwavelets, balanced multiwavelets, characterization of balancing condition, polynomial preservation/annihilation, moments, orthonormal bases

MSC numbers: 42C40, 42C15, 94A12