A Generalized Multiresolution Analysis and Affine Pseudoframes of Space L^2(R) Associated with Filter Banks

In recent years, frames have been the focus of active research, both in theory and applications. In the paper, the notion of affine pseudoframes for subspaces of L2(R) is introduced. We propose the concept of a generalized multiresolution structure (GMRA). We give an approach for constructing one GMRA of Paley-Wiener subspaces of L2(R). The sufficient condition for the existence of a class of multiple pseudoframes with filter banks for subspaces is obtained by virtue of a generalized multiresolution is proposed.