Geodesic
$\varphi$-Strong Approximation of Functions by Trigonometric Polynomials
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 52-63.

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

The rate of $\varphi$-strong approximation of periodic functions by trigonometric polynomials constructed on the basis of interpolating polynomials with equidistant nodes is considered.
Mots-clés : Fourier–Lagrange series
Keywords: group of deviations, best approximation, Dirichlet kernel. 
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R. A. Lasuriya. $\varphi$-Strong Approximation of Functions by Trigonometric Polynomials. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 52-63. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a5/

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

[2] G. G. Khardi, Dzh. E. Littlvud, G. Polia, Neravenstva, IL, M., 1948 | MR | Zbl

[3] V. Totik, “Notes on Fourier series: strong approximation”, J. Approx. Theory, 43:2 (1985), 105–111 | DOI | MR | Zbl

[4] V. V. Lipovik, “Pro poryadok nablizhennya v silnomu rozuminni periodichnikh funktsii deyakimi interpolyatsiinimi summami i summami Fur'e”, Dop. AN URSR. Cer. A, 5 (1971), 406–409

[5] V. V. Lipovik, V. I. Dukhovchenko, G. P. Gubanov, “O poryadke priblizheniya v silnom smysle periodicheskikh funktsii trigonometricheskimi polinomami”, Issledovaniya po sovremennym problemam summirovaniya i priblizheniya funktsii i ikh prilozheniyam, Vyp. 5, DGU, Dnepropetrovsk, 1974, 52–55

[6] G. Aleksich, Problemy skhodimosti ortogonalnykh ryadov, IL, M., 1963 | MR | Zbl

[7] G. Alexits, D. Králik, “Über die Approximation im Starken Sinne”, Acta Sci. Math. (Szeged), 26:1-2 (1965), 93–101 | MR | Zbl

[8] L. Leindler, “Über die Approximation im Starken Sinne”, Acta Math. Acad. Sci. Hungar., 16:1-2 (1965), 255–262 | DOI | MR | Zbl

[9] L. Leindler, Strong Approximation by Fourier Series, Akad. Kiadó, Budapest, 1985 | MR | Zbl

[10] L. D. Gogoladze, “O silnom summirovanii prostykh i kratnykh trigonometricheskikh ryadov”, Nekotorye voprosy teorii funktsii, T. 2, Tbilisi, 1981, 5–28

[11] A. I. Stepanets, N. L. Pachulia, “Gruppy otklonenii na mnozhestvakh $(\psi,\beta)$-differentsiruemykh funktsii”, Ukr. matem. zhurn., 40:1 (1988), 101–105 | MR | Zbl

[12] A. I. Stepanets, R. A. Lasuriya, “Kratnye summy Fure i $\varphi$-silnye srednie ikh uklonenii na klassakh $\overline\psi$-differentsiruemykh funktsii mnogikh peremennykh”, Ukr. matem. zhurn., 59:8 (2007), 1075–1093 | MR | Zbl

[13] R. A. Lasuriya, “Otsenki gruppy $\varphi$-otklonenii i silnaya summiruemost ryadov Teilora funktsii klassov $A^\psi H_\infty(D)$”, Matem. zametki, 83:5 (2008), 696–704 | DOI | MR | Zbl

[14] R. A. Lasuriya, Silnaya summiruemost ryadov Fure i approksimatsiya funktsii, AGU, Sukhum, 2010