Extension Principles for Dual Multiwavelet Frames of $$L_2(\mathbb {R}^s)$$ L 2 ( R s ) constructed from Multirefinable Generators

Abstract

In this work we prove that any pair of homogeneous dual multiwavelet frames of $$L_2(\mathbb {R}^s)$$ constructed from a pair of refinable function vectors gives rise to a pair of nonhomogeneous dual multiwavelet frames and vice versa. We also prove that the Mixed Oblique Extension Principle characterizes dual multiwavelet frames. Our results extend recent characterizations of affine dual frames derived from scalar refinable functions obtained in [3].