Discrete Fourier analysis on a dodecahedron and a tetrahedron

Details Discrete Fourier analysis on a dodecahedron and a tetrahedron Discrete Fourier analysis on a dodecahedron and a tetrahedron

2008-03-04

arxiv.org/abs/0803.0508v1

Mathematics

Numerical Analysis

31 pages, multiple figures

Scientific paper

A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is 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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