Abstract
In this article, compactly supported totally interpolating biorthogonal multiwavelet systems are studied. Necessary and sufficient conditions for such systems to have given approximation orders are stated in simple equations. It is shown that the shorter nontrivial filter component that has the minimum possible length for a given approximation order is uniquely determined up to a discrete parameter. Among systems with such property, we provide all totally interpolating biorthogonal stable multiwavelet systems of approximation orders 2 and 3 with minimal total length whose scaling vectors have minimal lengths as well.
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