Geodesic
Lebesgue functions corresponding to a~family of Lagrange interpolation polynomials
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 77-89.

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In this paper we obtain various explicit forms of the Lebesgue function corresponding to a family of Lagrange interpolation polynomials defined at an even number of nodes. We study these forms by using the derivatives up to the second order inclusive. We estimate exact values of Lebesgue constants for this family from below and above in terms of known parameters. In a particular case we obtain new simple formulas for calculating these estimates.
Mots-clés : Lagrange interpolation polynomials, Lebesgue functions and constants
Keywords: generalized Dirichlet kernel. 
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I. A. Shakirov. Lebesgue functions corresponding to a~family of Lagrange interpolation polynomials. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 77-89. http://geodesic.mathdoc.fr/item/IVM_2013_7_a6/

[1] Zigmund A., Trigonometricheskie ryady, v. 2, Mir, M., 1965 | MR

[2] Shakirov I. A., “O trigonometricheskom interpolyatsionnom polinome Lagranzha, imeyuschem minimalnuyu normu kak operator iz $C_{2\pi}$ v $C_{2\pi}$”, Izv. vuzov. Matem., 2010, no. 10, 60–68 | MR | Zbl

[3] Shakirov I. A., “Polnoe issledovanie funktsii Lebega, sootvetstvuyuschikh klassicheskim interpolyatsionnym polinomam Lagranzha”, Izv. vuzov. Matem., 2011, no. 10, 80–88 | MR | Zbl

[4] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR

[5] Dzyadyk V. K., Approksimatsionnye metody resheniya differentsialnykh i integralnykh uravnenii, Nauk. dumka, Kiev, 1988 | MR | Zbl

[6] Subbotin Yu. N., Telyakovskii S. A., “Asimptotika konstant Lebega periodicheskikh interpolyatsionnykh splainov s ravnootstoyaschimi uzlami”, Matem. sb., 191:8 (2000), 131–140 | DOI | MR | Zbl

[7] Babenko K. I., Osnovy chislennogo analiza, NITs Regulyarnaya i khaoticheskaya dinamika, Moskva–Izhevsk, 2002

[8] Kim V. A., “Tochnye konstanty Lebega dlya interpolyatsionnykh $\mathcal L$-splainov tretego poryadka”, Sib. matem. zhurn., 51:2 (2010), 330–341 | MR

[9] Baidakova N. V., “Otsenka sverkhu funktsii Lebega interpolyatsionnogo protsessa algebraicheskimi mnogochlenami po ravnomernym uzlam simpleksa”, Matem. zametki, 92:1 (2012), 19–26 | DOI | Zbl