Characterization of orthonormal high-order balanced multiwavelets in terms of moments
Bull. Korean Math. Soc. 2009 Vol. 46, No. 1, 183-198
Printed January 1, 2009
Soon-Geol Kwon
Sunchon National University
Abstract : 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
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