Sharp estimates for the convergence rate of Fourier–Bessel series
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 917-927
V. A. Abilov; F. V. Abilova; M. K. Kerimov. Sharp estimates for the convergence rate of Fourier–Bessel series. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 917-927. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sharp estimates are derived for the convergence rate of Fourier series in terms of Bessel functions of the first kind for some classes of functions characterized by a generalized modulus of continuity. The Kolmogorov $N$-width of these classes of functions are also estimated.

[1] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976

[2] Abilova F. V., “O nailuchshem priblizhenii funktsii algebraicheskimi mnogochlenami v srednem”, Doklady na Blgarskama Akademie na naukime. Comptes rendus de l Academie bulgare des Sciences, 46:12 (1993), 9–11 | MR

[3] Abilov V. A., Abilova F. V., “Priblizhenie funktsii summami Fure–Besselya”, Izv. vuzov. Matem., 2001, no. 8, 1–7 | MR

[4] Abilov V. A., Abilova F. V., Kerimov M. K., “Tochnye otsenki skorosti skhodimosti ryadov Fure na nekotorykh klassakh funktsii v prostranstve $\mathbb{L}_2((a,b), p(x))$”, Zh. vychisl. matem. i matem. fiz., 49:6 (2009), 966–980 | MR | Zbl

[5] Kolmogorov A. N., Izbrannye trudy. Matem. i mekhan., Nauka, M., 1987

[6] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969, 455 pp. | MR

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