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Localized Tight Frames and Fast Framelet Transforms on the Simplex

Abstract

This paper constructs a continuous localized tight frame on a two-dimensional simplex T2T^{2} using orthogonal polynomials. We then use quadrature rules on T2T^{2} to construct discrete tight framelets. Fast algorithms for discrete tight framelet transforms on T2T^{2} are given, which have the same computational steps as the fast Fourier transforms on the simplex T2T^{2}.

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