Construction of a sort of multiple pseudoframes for subspaces with filter banks

Abstract

During the last 20 years the theory of frames has been growing rapidly, since several new applications have been developed. In this paper, the notion of subspace multiple pseudoframes of translation of space L 2 ( R ) is introduced. A method for constructing one generalized multiresolution structure of Paley–Wiener subspaces of L 2 ( R ) is provided based on the theory of filter banks. The sufficient condition for the existence of a class of multiple pseudoframes with filter banks is obtained by virtue of the generalized multiresolution structure. Lastly, a frame-like decomposition of space L 2 ( R ) is given based on the multiple pseudoframes for subspaces. Relation to some physical theories such as the quantum golden field theory is also discussed.