Geodesic
On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 978-989

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

Approximation properties of the de la Vallée Poussin means $V_{n+m,N}^\alpha(f,x)$ of Fourier–Meixner sums are studied. In particular, for $an\le m\le bn$ and $n+m\le \lambda N$ the existence of a constant $c(a,b,\alpha,\lambda)$ is established such that $\|V^\alpha_{n+m,N}(f)\|\le c(a,b,\alpha,\lambda)\|f\|$, where $\|f\|$ is the uniform norm of the function $f$ on the grid $\Omega_\delta$.
Keywords: approximation properties, Meixner polynomials, Fourier series
Mots-clés : de la Vallée Poussin means. 
R. M. Gadzhimirzaev. On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 978-989. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a58/
@article{SEMR_2024_21_2_a58,
     author = {R. M. Gadzhimirzaev},
     title = {On the uniform boundedness of {Vall\'ee} {Poussin} means in the system of {Meixner} polynomials},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {978--989},
     year = {2024},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a58/}
}
TY  - JOUR
AU  - R. M. Gadzhimirzaev
TI  - On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 978
EP  - 989
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a58/
LA  - ru
ID  - SEMR_2024_21_2_a58
ER  - 
%0 Journal Article
%A R. M. Gadzhimirzaev
%T On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 978-989
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a58/
%G ru
%F SEMR_2024_21_2_a58

[1] Z.D. Gadzhieva, Mixed Series in Meixner Polynomials, Cand. Sci. (Phys.-Math.) Dissertation, Saratov Gos. Univ., Saratov, 2004

[2] Z.D. Gadzhieva, F.E. Esetov, M.N. Yuzbekova, “Approximation properties of Fourier-Meixner sums on $[0,\infty)$”, Dagestan State Pedagogical University, J. Est.Toch. Nauki, 3(32) (2015), 6–8

[3] R.M. Gadzhimirzaev, “Approximative properties of Fourier-Meixner sums”, Probl. Anal. Issues Anal., 7(25):1 (2018), 23–40 | MR | Zbl

[4] R.M. Gadzhimirzaev, “Estimate of the Lebesgue function of Fourier sums in terms of modified Meixner polynomials”, Math. Notes, 106:4 (2019), 526–536 | DOI | MR | Zbl

[5] I.I. Sharapudinov, I.A. Vagabov, “Convergence of the Vallée Poussin means for Fourier-Jacobi sums”, Math. Notes, 60:4 (1996), 425–437 | DOI | MR | Zbl

[6] I.I. Sharapudinov, “Boundedness in $C[-1,1]$ of the de la Vallée Poussin means for discrete Chebyshev-Fourier sums”, Sb. Math., 187:1 (1996), 141–158 | DOI | MR | Zbl

[7] F.M. Korkmasov, “Approximate properties of the de la Vallée Poussin means for the discrete Fourier-Jacobi sums”, Sib. Math. J., 45:2 (2004), 273–293 | DOI | MR | Zbl

[8] G. Mastroianni, W. Themistoclakis, “De la Vallée Poussin means and Jackson's theorem”, Acta Sci. Math., 74:1-2 (2008), 147–170 | MR | Zbl

[9] W. Themistoclakis, “Weighted $L^1$ approximation on $[-1,1]$ via discrete de la Vallée Poussin means”, Math. Comput. Simul., 147 (2018), 279–292 | DOI | MR | Zbl

[10] I.I. Sharapudinov, Polynomials orthogonal on the grid. Theory and Applications, DSU publishing, Makhachkala, 1997

[11] I.I. Sharapudinov, “Asymptotics and weighted estimates of Meixner polynomials orthogonal on the gird $\{0,\delta, 2\delta, \ldots\}$”, Math. Notes, 62:4 (1997), 501–512 | DOI | MR | Zbl

[12] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, New York, 1972 | MR

[13] R.M. Gadzhimirzaev, “Approximation properties of de la Vallée Poussin means of partial Fourier series in Meixner-Sobolev polynomials”, Mat. Sbornik, 215:9 (2024), 77–98 | MR