Nonstationary refinable functions based on generalized Bernstern polynomials

In this paper, we introduce a new family of non-stationary refinable functions from Generalized Bernstein Polynomials, which include a class of nonstationary refinable functions generated from the family of masks for the pseudo splines of type II (see [17]). Furthermore, a proof of the convergence of non-stationary cascade algorithms associated with the new masks is completed. We then construct symmetric compacted supported non-stationary C^∞ tight wavelet frames in L₂(ℝ) with the spectral frame approximation order.