The characterization of a class of affine pseudoframes of space L2(R) with refinable functions

The notion of a generalized multiresolution structure (GMS) of L²(R) is formulated. The definition of multiple pseudoframes for subspaces of L²(R) is presented. The construction of a 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.