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Analysis of Framelet Transforms on Simplex

6 January 2017
Yu Guang Wang
Hou-Ying Zhu
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Abstract

In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex T2T^2T2 in R2\mathbb{R}^{2}R2. We give the framelet transforms --- decomposition and reconstruction of the coefficients for framelets of a function on T2T^2T2. We prove that the reconstruction is exact when the framelets are tight. We give an example of construction of framelets and show that the framelet transforms can be computed as fast as FFT.

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