Subspace Affine Dual Multiple Frames with Multi-filter Functions and a General Multiresolution Structure

Abstract

Abstract Frames have become the focus of active research, both in theory and in applications. The notion of a generalized multiresolution structure of L2(R) is formulated. The definition of dual multiple frames for subspaces of L2(R) is proposed. The construction of a generalralized multiresolution structure (GMS) of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is obtained based on such a GMS. A sufficient condition on the existence of dual multiple pseodoframes is presented by means of paraunitary vector filter bank theory.