Abstract
Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudo- -frames 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.
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