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Chebyshev Polynomials and the Proper Decomposition of Functions

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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 \(\mathcal{L}_g^2\), 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 B3, C3, and D3.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. D. Lyakhovsky

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  1. V. D. Lyakhovsky
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Correspondence to V. D. Lyakhovsky.

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Conflicts of interest. The author declares no conflicts of interest.

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Lyakhovsky, V.D. Chebyshev Polynomials and the Proper Decomposition of Functions. Theor Math Phys 200, 1147–1157 (2019). https://doi.org/10.1134/S0040577919080075

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  • DOI: https://doi.org/10.1134/S0040577919080075

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