Geodesic
Extremal Properties of Certain Trigonometric Functions and Chebyshev Polynomials
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 350-355

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For a wide class of symmetric trigonometric polynomials, the minimal deviation property is established. As a corollary, the extremal property is proved for the components of the Chebyshev polynomial mappings corresponding to symmetric algebras $A_\alpha$.
Keywords: Chebyshev and trigonometric polynomials, minimal deviation property, symmetric algebras, complex Lie algebra. 
I. V. Belyakov. Extremal Properties of Certain Trigonometric Functions and Chebyshev Polynomials. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 350-355. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a3/
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[1] V. I. Smirnov, N. A. Lebedev, Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1964 | MR | Zbl

[2] A. P. Veselov, “Integriruemye polinomialnye otobrazheniya i algebry Li”, Geometriya, differentsialnye uravneniya i mekhanika, Izd-vo MGU, M., 1986, 59–63 | MR

[3] A. P. Veselov, “Integriruemye otobrazheniya i algebry Li”, Dokl. AN SSSR, 292:6 (1987), 1289–1291 | MR | Zbl

[4] M. E. Hoffman, W. D. Withers, “Generalized Chebyshev polinomials, associated with affine Weyl groups”, Trans. Amer. Math. Soc., 308:1 (1988), 91–104 | DOI | MR | Zbl

[5] A. G. Kurosh, Kurs vysshei algebry, Nauka, M., 1975 | Zbl

[6] I. V. Belyakov, A. M. Stepin, “Ekstremalnye svoistva mnogomernykh otobrazhenii Chebysheva”, Vestn. MGU. Ser. 1. Matem., mekh., 1996, no. 6, 22–24 | MR | Zbl

[7] I. V. Belyakov, Mnogomernye otobrazheniya Chebysheva, Diss. ... kand. fiz.-matem. nauk, M., MGU, 1997

[8] I. V. Belyakov, “Minimalnoe uklonenie ot nulya otobrazhenii Chebysheva, sootvetstvuyuschikh ravnostoronnemu treugolniku”, Matem. zametki, 59:6 (1996), 919–922 | MR | Zbl