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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Discrete Fourier analysis on a dodecahedron and a tetrahedron


Authors: Huiyuan Li and Yuan Xu
Journal: Math. Comp. 78 (2009), 999-1029
MSC (2000): Primary 41A05, 41A10
Published electronically: August 27, 2008
MathSciNet review: 2476568
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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$.


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Additional Information

Huiyuan Li
Affiliation: Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
Email: hynli@mail.rdcps.ac.cn

Yuan Xu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222.
Email: yuan@math.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02156-X
PII: S 0025-5718(08)02156-X
Keywords: Discrete Fourier series, trigonometric, Lagrange interpolation, dodecahedron, tetrahedron
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
Article copyright: © Copyright 2008 American Mathematical Society