The characterization of a class of subspace pseudoframes with arbitrary real number translations

In this article, the notion of generalized multiresolution structure is introduced. The concept of subspace pseudoframes with arbitrary real number translations is proposed. A new method for constructing a generalized multiresolution structure in Paley–Wiener subspace of L2ðRÞ is presented. A pyramid decomposition scheme is established based on such a generalized multiresolution structure. Finally, affine frames of space L2ðRÞ with arbitrary real number translations are obtained by virtue of the subspace pseudoframes and the pyramid decomposition scheme. Relation to some physical theories such as quarks confinement is also investigated.