The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

摘要

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace L~2(R~2) is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L~2(R~2) is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L~2(R~2) based on a BGMS is established.