Discrete Fourier analysis on a dodecahedron and a tetrahedron
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- by Huiyuan Li and Yuan Xu PDF
- Math. Comp. 78 (2009), 999-1029 Request permission
Abstract:
A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron are deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the interpolation is shown to be in the order of $(\log n)^3$.References
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Additional Information
- Huiyuan Li
- Affiliation: Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
- MR Author ID: 708582
- Email: hynli@mail.rdcps.ac.cn
- Yuan Xu
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222.
- MR Author ID: 227532
- Email: yuan@math.uoregon.edu
- Received by editor(s): April 10, 2007
- Received by editor(s) in revised form: February 29, 2008
- Published electronically: August 27, 2008
- Additional Notes: The first authors were supported by NSFC Grants 10601056, 10431050 and 60573023. The second author was supported by NSF Grant DMS-0604056
- © Copyright 2008 American Mathematical Society
- Journal: Math. Comp. 78 (2009), 999-1029
- MSC (2000): Primary 41A05, 41A10
- DOI: https://doi.org/10.1090/S0025-5718-08-02156-X
- MathSciNet review: 2476568