Multivariate Symmetric Interpolating Scaling Vectors with Duals

Abstract

In this paper we introduce an algorithm for the construction of compactly supported interpolating scaling vectors on ℝd with certain symmetry properties. In addition, we give an explicit construction method for corresponding symmetric dual scaling vectors and multiwavelets. As the main ingredients of our recipe we derive some implementable conditions for accuracy, symmetry, and biorthogonality of a scaling vector in terms of its mask. Our method is substantiated by several bivariate examples for quincunx and box-spline dilation matrices.