Affine pseudoframes for subspaces of L2(R) associated with a generalized multiresolution structure

In this paper, the notion of an m-band generalized multiresolution structure (GMS) of L2(R) is introduced. We give the definition and the characterization of affine pseudoframes for subspaces. The construction of a GMS of Paley–Wiener subspaces of L2(R) is investigated. The pyramid decomposition scheme is derived based on such a GMS. As a major new contribution the construction of affine frames for L2(R) based on a GMS is presented.