Subspace affine pseudoframes with a generalized multiresolution structure and the pyramid decomposition scheme

The rise of frame theory in applied mathematics is due to the flexibility and redundancy of frames. In this work, the notion of a generalized multiresolution structure of L2(R) is proposed. The definition of multiple pseudoframes for subspaces of L2(R) is given. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is derived based on such a generalized multiresolution structure. The pyramid decomposition scheme is also obtained.