This article is cited in 1 paper

Chebyshev polynomials and the proper decomposition of functions

V. D. Lyakhovsky

Saint Petersburg State University, St. Petersburg, Russia

Abstract: 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, orthogonal polynomial, discrete Fourier series, function decomposition.

Received: 29.11.2018
Revised: 29.11.2018

DOI: 10.4213/tmf9666

 English version: Theoretical and Mathematical Physics, 2019, 200:2, 1147–1157

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