I. I. Sharapudinov, “Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials”, Mat. Zametki, 84:3 (2008), 452–471; Math. Notes, 84:3 (2008), 417

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Matematicheskie Zametki, 2008, Volume 84, Issue 3, Pages 452–471
DOI: https://doi.org/10.4213/mzm5541 (Mi mzm5541)

This article is cited in 24 scientific papers (total in 24 papers)

Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials

I. I. Sharapudinov

Daghestan Scientific Centre of the Russian Academy of Sciences

Full-text PDF (514 kB) Citations (24)

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DOI: https://doi.org/10.4213/mzm5541

Abstract: 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, Legendre polynomial, Fourier–Legendre series, Vallée-Poussin means, Jacobi polynomial, Hermite interpolation polynomial.

Received: 04.04.2007

English version:
Mathematical Notes, 2008, Volume 84, Issue 3, Pages 417–434
DOI: https://doi.org/10.1134/S0001434608090125

Bibliographic databases:

UDC: 517.518.82

Language: Russian

Citation: I. I. Sharapudinov, “Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials”, Mat. Zametki, 84:3 (2008), 452–471; Math. Notes, 84:3 (2008), 417–434

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm5541

https://doi.org/10.4213/mzm5541

https://www.mathnet.ru/eng/mzm/v84/i3/p452

This publication is cited in the following 24 articles:

R. M. Gadzhimirzaev, “Approximation properties of the Vallée-Poussin means similar to the partial sums of Fourier series in Laguerre–Sobolev polynomials”, Siberian Math. J., 63:3 (2022), 451–465
Md. N. Islam, I. Kaish, Md. N. Akhtar, M. A. Navascués, “Fractal Sobolev systems of functions associated with orthonormal systems of functions”, Asian-European J. Math., 15:11 (2022)
M. G. Magomed-Kasumov, Trends in Mathematics, Operator Theory and Differential Equations, 2021, 107
I. I. Sharapudinov, “Sobolev-orthogonal systems of functions and some of their applications”, Russian Math. Surveys, 74:4 (2019), 659–733
I. I. Sharapudinov, “Sobolev-orthogonal systems of functions associated with an orthogonal system”, Izv. Math., 82:1 (2018), 212–244
Sharapudinov I.I., Magomed-Kasumov M.G., “On Representation of a Solution to the Cauchy Problem By a Fourier Series in Sobolev-Orthogonal Polynomials Generated By Laguerre Polynomials”, Differ. Equ., 54:1 (2018), 49–66
L. K. Dodunova, A. A. Ageikin, “Approximation of analytic functions by universal Vallee-Poussin sums on the Chebyshev polynomials”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 24 (2018), 12–23
I. I. Sharapudinov, M. G. Magomed-Kasumov, “On Vallée-Poissin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums”, Russian Math. (Iz. VUZ), 62:9 (2018), 60–71
I. I. Sharapudinov, “Sobolev orthogonal polynomials generated by Jacobi and Legendre polynomials, and special series with the sticking property for their partial sums”, Sb. Math., 209:9 (2018), 1390–1417
Sharapudinov I.I., “Sobolev Orthogonal Polynomials Associated With Chebyshev Polynomials of the First Kind and the Cauchy Problem For Ordinary Differential Equations”, Differ. Equ., 54:12 (2018), 1602–1619
I. I. Sharapudinov, “Approximation Properties of Fourier Series of Sobolev Orthogonal Polynomials with Jacobi Weight and Discrete Masses”, Math. Notes, 101:4 (2017), 718–734
I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Raznostnye uravneniya i polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Meiksnera”, Vladikavk. matem. zhurn., 19:2 (2017), 58–72
I. I. Sharapudinov, “Special series in Laguerre polynomials and their approximation properties”, Siberian Math. J., 58:2 (2017), 338–362
I. I. Sharapudinov, “Obraschenie preobrazovaniya Laplasa posredstvom obobschennykh spetsialnykh ryadov po polinomam Lagerra”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 7–20
I. I. Sharapudinov, Z. D. Gadzhieva, “Polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Meiksnera”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 310–321
R. M. Gadzhimirzaev, “Ryady Fure po polinomam Meiksnera, ortogonalnym po Sobolevu”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:4 (2016), 388–395
I. I. Sharapudinov, “Asimptoticheskie svoistva polinomov, ortogonalnykh po Sobolevu, porozhdennykh polinomami Yakobi”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 6, 1–24
I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Sistemy funktsii, ortogonalnykh otnositelno skalyarnykh proizvedenii tipa Soboleva s diskretnymi massami, porozhdennykh klassicheskimi ortogonalnymi sistemami”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 6, 31–60
I. I. Sharapudinov, M. G. Magomed-Kasumov, S. R. Magomedov, “Polinomy, ortogonalnye po Sobolevu, assotsiirovannye s polinomami Chebysheva pervogo roda”, Dagestanskie elektronnye matematicheskie izvestiya, 2015, no. 4, 1–14
T. I. Sharapudinov, “Diskretnye polinomy, ortogonalnye po Sobolevu, assotsiirovannye s polinomami Chebysheva, ortogonalnymi na ravnomernoi setke”, Dagestanskie elektronnye matematicheskie izvestiya, 2015, no. 4, 15–20

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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