Geodesic
Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials
Matematičeskie zametki, Tome 84 (2008) no. 3, pp. 452-471.

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

We estimate the order of weighted approximations of functions and their derivatives by using the means of mixed series of Legendre polynomials. As the main result, we obtain estimates of the order of approximation of a function and its derivatives by the Vallée-Poussin means and their derivatives.
Keywords: approximation of functions, Vallée-Poussin means
Mots-clés : Legendre polynomial, Fourier–Legendre series, Jacobi polynomial, Hermite interpolation polynomial. 
@article{MZM_2008_84_3_a11,
     author = {I. I. Sharapudinov},
     title = {Approximation {Properties} of the {Vall\'ee-Poussin} {Means} of {Partial} {Sums} of a {Mixed} {Series} of {Legendre} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {452--471},
     publisher = {mathdoc},
     volume = {84},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/}
}
TY  - JOUR
AU  - I. I. Sharapudinov
TI  - Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials
JO  - Matematičeskie zametki
PY  - 2008
SP  - 452
EP  - 471
VL  - 84
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/
LA  - ru
ID  - MZM_2008_84_3_a11
ER  - 
%0 Journal Article
%A I. I. Sharapudinov
%T Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials
%J Matematičeskie zametki
%D 2008
%P 452-471
%V 84
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/
%G ru
%F MZM_2008_84_3_a11
I. I. Sharapudinov. Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials. Matematičeskie zametki, Tome 84 (2008) no. 3, pp. 452-471. http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/

[1] I. I. Sharapudinov, “Priblizhenie funktsii s peremennoi gladkostyu summami Fure–Lezhandra”, Matem. sb., 191:5 (2000), 143–160 | MR | Zbl

[2] I. I. Sharapudinov, “Smeshannye ryady po ultrasfericheskim polinomam i ikh approksimativnye svoistva”, Matem. sb., 194:3 (2003), 115–148 | MR | Zbl

[3] I. I. Sharapudinov, “Approksimativnye svoistva operatorov $\mathscr Y_{n+2r}(f)$ i ikh diskretnykh analogov”, Matem. zametki, 72:5, 765–795 | MR | Zbl

[4] I. I. Sharapudinov, Smeshannye ryady po ortogonalnym polinomam. Teoriya i prilozheniya, DNTs RAN, Makhachkala, 2004

[5] I. I. Sharapudinov, “Approksimativnye svoistva smeshannykh ryadov po polinomam Lezhandra na klassakh $W^r$”, Matem. sb., 197:3 (2006), 135–154 | MR | Zbl

[6] S. A. Telyakovskii, “Dve teoremy o priblizhenii funktsii algebraicheskimi mnogochlenami”, Matem. sb., 70:2 (1966), 252–265 | MR | Zbl

[7] I. Z. Gopengauz, “K teoreme A. F. Timana o priblizhenii funktsii mnogochlenami na konechnom otrezke”, Matem. zametki, 1:2 (1967), 163–172 | MR | Zbl

[8] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962 | MR | Zbl