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

DOI:
https://doi.org/10.1090/S0025-5718-08-02156-X

Published electronically:
August 27, 2008

MathSciNet review:
2476568

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Abstract | References | Similar Articles | Additional Information

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 .

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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:
https://doi.org/10.1090/S0025-5718-08-02156-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