Orthogonal multiwavelets of multiplicity four

We consider solutions of a system of refinement equations with a 4 × 1 function vector and three nonzero 4 × 4 coefficient matrices. We give explicit expressions of coefficient matrices such that the refinement function vector and the corresponding wavelet vector have properties of short support [0, 2], symmetry or antisymmetry, and orthogonality. The properties of convergence of the subdivision scheme, approximation order, and smoothness of the refinement functions are also discussed.