Geodesic
Chebyshev polynomials and the~proper decomposition of functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 259-268

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We study the equivalence property of scalar products, based on which we can find the rows of the Chebyshev polynomial sets. For each function in the space $\mathcal L^2_{\mathfrak g}$, the approximation by a row of Chebyshev polynomials is characterized by the standard deviation. In the case of simple algebras, the sets of standard Chebyshev polynomials ensure rapid convergence of the rows. The presented calculation algorithm produces correct results for the algebras $B_3$, $C_3$, and $D_3$.
Keywords: root system, Chebyshev multivariate polynomial, discrete Fourier series, function decomposition.
Mots-clés : orthogonal polynomial 
@article{TMF_2019_200_2_a6,
     author = {V. D. Lyakhovsky},
     title = {Chebyshev polynomials and the~proper decomposition of functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {259--268},
     publisher = {mathdoc},
     volume = {200},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a6/}
}
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V. D. Lyakhovsky. Chebyshev polynomials and the~proper decomposition of functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 259-268. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a6/