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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2006_80_3_a3,
     author = {I. V. Belyakov},
     title = {Extremal {Properties} of {Certain} {Trigonometric} {Functions} and {Chebyshev} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {350--355},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a3/}
}
TY  - JOUR
AU  - I. V. Belyakov
TI  - Extremal Properties of Certain Trigonometric Functions and Chebyshev Polynomials
JO  - Matematičeskie zametki
PY  - 2006
SP  - 350
EP  - 355
VL  - 80
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a3/
LA  - ru
ID  - MZM_2006_80_3_a3
ER  - 
%0 Journal Article
%A I. V. Belyakov
%T Extremal Properties of Certain Trigonometric Functions and Chebyshev Polynomials
%J Matematičeskie zametki
%D 2006
%P 350-355
%V 80
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a3/
%G ru
%F MZM_2006_80_3_a3
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/

[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