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Mat. Zametki, 2008, Volume 84, Issue 3, Pages 452–471 (Mi mz5541)  

This article is cited in 20 scientific papers (total in 20 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

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

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

Full text: PDF file (514 kB)
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English version:
Mathematical Notes, 2008, 84:3, 417–434

Bibliographic databases:

UDC: 517.518.82
Received: 04.04.2007

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

    This publication is cited in the following articles:
    1. I. I. Sharapudinov, “The basis property of the Legendre polynomials in the variable exponent Lebesgue space $L^{p(x)}(-1,1)$”, Sb. Math., 200:1 (2009), 133–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. I. I. Sharapudinov, T. I. Sharapudinov, “Mixed Series of Jacobi and Chebyshev Polynomials and Their Discretization”, Math. Notes, 88:1 (2010), 112–139  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. I. Sharapudinov, “Approximating smooth functions using algebraic-trigonometric polynomials”, Sb. Math., 201:11 (2010), 1689–1713  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. 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  mathnet  crossref  elib
    5. 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  mathnet  crossref  elib
    6. I. I. Sharapudinov, “Nekotorye spetsialnye ryady po obschim polinomam Lagerra i ryady Fure po polinomam Lagerra, ortogonalnym po Sobolevu”, Dagestanskie elektronnye matematicheskie izvestiya, 2015, no. 4, 31–73  mathnet  crossref  elib
    7. 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  mathnet  crossref  mathscinet  elib
    8. 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  mathnet  crossref  mathscinet  elib
    9. I. I. Sharapudinov, “Asimptoticheskie svoistva polinomov, ortogonalnykh po Sobolevu, porozhdennykh polinomami Yakobi”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 6, 1–24  mathnet  crossref  elib
    10. 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  mathnet  crossref  elib
    11. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    12. 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  mathnet
    13. I. I. Sharapudinov, “Special series in Laguerre polynomials and their approximation properties”, Siberian Math. J., 58:2 (2017), 338–362  mathnet  crossref  crossref  isi  elib  elib
    14. I. I. Sharapudinov, “Obraschenie preobrazovaniya Laplasa posredstvom obobschennykh spetsialnykh ryadov po polinomam Lagerra”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 7–20  mathnet  crossref
    15. I. I. Sharapudinov, “Sobolev-orthogonal systems of functions associated with an orthogonal system”, Izv. Math., 82:1 (2018), 212–244  mathnet  crossref  crossref  adsnasa  isi  elib
    16. 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  crossref  mathscinet  zmath  isi  scopus
    17. 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  mathnet  crossref
    18. 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  mathnet  crossref  isi
    19. 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  mathnet  crossref  crossref  adsnasa  isi  elib
    20. 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  crossref  mathscinet  isi  scopus
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