REGULARITY AND VANISHING MOMENTS OF MULTIWAVELETS

Abstract

We introduce the Wiener space and then consider wavelets which are not necessarily compactly supported but have a decay condition at infinity. Under the Wiener condition, several scaling functions and their dual functions have the same rate of decay at infinity. Furthermore, multiwavelets and their bi-orthogonal multiwavelets have the same rate of decay at infinity and the same number of vanishing moments.