Symmetric MRA tight wavelet frames with three generators and high vanishing moments

Let ϕ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of ϕ are stable, in this paper we prove that one can always construct three wavelet functions ψ1, ψ2, and ψ3 such that