Symmetry properties of totally interpolating biorthogonal multiwavelet systems

We consider compactly supported totally interpolating biorthogonal multiwavelet systems in this article. Necessary and sufficient conditions for such systems to have given approximation orders are stated. 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. We provide an example of such system with approximation order 4. Although there is no symmetric or antisymmetric totally interpolating biorthogonal multiwavelet systems, one can find uniquely totally interpolating biorthogonal multiwavelet system having a suitable symmetry property in terms of coefficients of the shorter filter. When a high approximation order 11, an example having this symmetry property is provided.