Abstract

The duality principle, ultimately a statement about adjoint operators, is a universal principle in frame theory. We take a broad perspective on the duality principle and discuss how the mixed unitary extension principle for MRA-wavelet frames can be viewed as the duality principle in a sequence space. This leads to a construction scheme for dual MRA-wavelet frames which is strikingly simple in the sense that it only requires the completion of an invertible constant matrix. Under minimal conditions on the multiresolution analysis our construction guarantees the existence and easy constructability of  multivariate non-tensor product dual MRA-wavelet frames of compactly supported wavelets. These can for instance be of interest for multiscale representations of surfaces.