d-Refinable (dual) pseudo-splines and their regularities

In this paper, we introduce the concept of d-dilation (dual) pseudo-splines in L2(ℝ) with dilation d ≥ 2, characterize the linear independence of the integer shifts, the subdivision schemes of polynomial reproduction and Holder regularity for (dual) pseudo-splines with general dilation. We present a new method to determine the Holder regularity of refinable functions with general dilation d ≥ 2. Furthermore, we compare the regularities between pseudo-splines and dual ones.