Generalized frame multiresolution analysis of abstract Hilbert spaces and its applications

We define a very generic class of multiresolution analysis of abstract Hilbert spaces. Their core subspaces have a frame produced by the action of an abelian unitary group on a perhaps infinite subset of the core subspace. which rye call frame multiscaling vector set. We characterize the associated frame multiwavelet vector sets by generalizing the concept of the low and high pass filters and the Quadrature Mirror filter condition. We include an extensive overview of related work of other and Re conclude with some examples.