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Analysis of Framelet Transforms on a Simplex

  • Yu Guang Wang
  • Houying Zhu
Chapter

Abstract

In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex T2 in \(\mathbb {R}^{2}\). We give the framelet transforms—decomposition and reconstruction of the coefficients for framelets of a function on T2. 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.

Notes

Acknowledgements

The authors thank the anonymous referees for their valuable comments. We are grateful to Kinjal Basu, Yuan Xu and Xiaosheng Zhuang for their helpful discussions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia
  2. 2.School of Mathematics and StatisticsThe University of MelbourneMelbourneAustralia

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