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 quarternary generalized multiresol- ution structure (TGMS) of subspace is proposed. The characteristics of quarternary affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.
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