M-Band Scaling Function with Filter Having Vanishing Moments Two and Minimal Length

In this paper we consider the H¨older continuity, local linearity, linear independence, and interpolation problem of the M-band scaling function, with a filter having vanishing moments two and minimal length. In particular, we find some new properties that are not true when Ms2, such as local linearity, local linear dependence, differentiability at adjoint M-adic points, and interpolation problem at integer knots.