Construction of refinable function vector via GTST

The concept of general two-scale similarity transform (GTST) is introduced. By applying GTST, we present an algorithm of constructing a class of compactly supported refinable function vector. In addition, we prove that GTST can preserve the symmetry of the given a refinable function vector, and give a sufficient condition that the corresponding transform matrices M(z) and N(z) satisfy when GTST can preserve symmetry. Some examples are given.