Uniform approximation by polynomials on compacta of special form
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 47-51
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
A lower estimate of the least deviations is obtained and polynomials of the best uniform approximation are found for some functions given on compact sets of the complex plane containing full preimages $Q^{-1}(v_{j})$ of several points $v_{j}\in\mathbb{C}$ for some polynomial $Q(z)$ of a complex variable.
[1] Kamo S.O., Borodin P.A., “Mnogochleny Chebysheva dlya mnozhestv Zhyulia”, Vestn. Mosk. un-ta. Matem. Mekhan., 1994, no. 5, 65–67
[2] Borodin P.A., “Ob odnom uslovii na mnogochlen, dostatochnom dlya minimalnosti ego normy na zadannom kompakte”, Vestn. Mosk. un-ta. Matem. Mekhan., 2006, no. 4, 14–18
[3] Pakovich F., “On polynomials sharing preimages of compact sets, and related questions”, Geom. and Funct. Anal., 18:1 (2007), 163–183 | DOI | MR
[4] Dzyadyk V.K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1997 | MR