Geodesic
Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 966-980 
V. A. Abilov; F. V. Abilova; M. K. Kerimov. Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 966-980. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a3/
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     title = {Sharp estimates for the convergence rate of {Fourier} series in terms of orthogonal polynomials in $L_2((a,b),p(x))$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space $L_2((a,b),p(x))$. Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered.

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Gostekhteorizdat, M., 1953

[2] Vladimirov B. C., Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | MR | Zbl

[3] Sveshnikov A. G., Bogolyubov A. N., Kravtsov V. V., Lektsii po matematicheskoi fizike, Nauka, M., 2004

[4] Babenko K. I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

[5] Bakhvalov N.S., Chislennye metody, Nauka, M., 1973 | MR | Zbl

[6] Lokutsievskii O. V., Gavrikov M. B., Nachala chislennogo analiza, TOO “Yanus”, M., 1995 | MR

[7] Abilov B. A., “Esche raz ob odnom ekstremalnom svoistve klassicheskikh ortogonalnykh mnogochlenov”, Dokl. Bolgarskoi AN, 45:6 (1992), 33–34 | MR | Zbl

[8] Abilova F. V., “O nailuchshem priblizhenii funktsii algebraicheskimi mnogochlenami v srednem”, Dokl. Bolgarskoi AN, 46:12 (1993), 9–11 | MR | Zbl

[9] Abilov V. A., Abilova F. V., “Priblizhenie funktsii algebraicheskimi mnogochlenami v srednem”, Izv. vuzov. Matematika, 1997, no. 3, 61–63 | MR | Zbl

[10] Abilov B. A., “Otsenka poperechnika odnogo klassa funktsii v prostranstve $L_2((a,b),p(x))$”, Dokl. Bolgarskoi AN, 45:10 (1992), 23–24 | MR | Zbl

[11] Abilov V. A., Kerimov M. K., “Nekotorye voprosy razlozheniya funktsii v dvoinye ryady Fure–Besselya”, Zh. vychisl. matem. i matem. fiz., 44:12 (2004), 2128–2149 | MR | Zbl

[12] Rafalson S. Z., “Nailuchshee priblizhenie funktsii v metrikakh $L^2_{p(x)}$ algebraicheskimi mnogochlenami i koeffitsienty Fure po ortogonalnym mnogochlenam”, Vestn. LGU. Mekhan. i matem., 1969, no. 7, 68–79 | MR

[13] Nikiforov A. F., Uvarov I. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1978 | MR

[14] Sege G., Ortogonalnye mnogochleny, Perev. s angl. B. C. Videnskogo s predisloviem i dopolneniyami Ya. L. Geronimusa, Fizmatlit, M., 1962

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

[16] Kolmogorov A. N., Izbrannye trudy. T. 1. Matematika i mekhanika, Nauka, M., 1987 | MR

[17] Korneichuk H. P., Tochnye konstanty v teorii priblizhenii, Nauka, M., 1987

[18] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[19] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Nauka, M., 1960