Regularity of refinable function vectors

We study the existence and regularity of compactly supported solutions phi=(phi(v))(v=0)(r-1) of vector refinement equations. The space spanned by the translates of phi(v), can only provide approximation order if the refinement mask P has certain particular factorization properties. We show, how the factorization of P can lead to decay of \phi(v)(u)\ as \u\ --> infinity. The results on decay are used to prove uniqueness of solutions and convergence of the cascade algorithm.