RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2000, Volume 191, Number 5, Pages 143–160 (Mi msb480)  

This article is cited in 21 scientific papers (total in 21 papers)

Approximation of functions of variable smoothness by Fourier–Legendre sums

I. I. Sharapudinov

Daghestan State University

Abstract: Assume that $0<\mu\leqslant 1$, and let $r\geqslant 1$ be an integer. Let $\Delta =\{a_1,…,a_l\}$, where the $a_i$ are points in the interval $(-1,1)$. The classes $S^rH^\mu_\Delta$ and $S^rH^\mu_\Delta(B)$ are introduced. These consist of functions with absolutely continuous $(r-1)$th derivative on $[-1,1]$ such that their $r$th and $(r+1)$th derivatives satisfy certain conditions outside the set $\Delta$. It is proved that for $0<\mu<1$ the Fourier–Legendre sums realize the best approximation in the classes $S^rH^\mu_\Delta(B)$. Using the Fourier–Legendre expansions, polynomials $\mathscr Y_{n+2r}$ of order $n+2r$ are constructed that possess the following property: for $0<\mu<1$ the $\nu$th derivative of the polynomial $\mathscr Y_{n+2r}$ approximates $f^{(\nu)}(x)$ $(f\in S^rH^\mu_\Delta)$ on $[-1,1]$ to within $O(n^{\nu+1-r-\mu})$, and the accuracy is of order $O(n^{\nu-r-\mu})$ outside $\Delta$.

DOI: https://doi.org/10.4213/sm480

Full text: PDF file (298 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:5, 759–777

Bibliographic databases:

UDC: 517.98
MSC: 42C10, 41A10
Received: 10.06.1998 and 17.05.1999

Citation: I. I. Sharapudinov, “Approximation of functions of variable smoothness by Fourier–Legendre sums”, Mat. Sb., 191:5 (2000), 143–160; Sb. Math., 191:5 (2000), 759–777

Citation in format AMSBIB
\Bibitem{Sha00}
\by I.~I.~Sharapudinov
\paper Approximation of functions of variable smoothness by Fourier--Legendre sums
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 5
\pages 143--160
\mathnet{http://mi.mathnet.ru/msb480}
\crossref{https://doi.org/10.4213/sm480}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1773772}
\zmath{https://zbmath.org/?q=an:0971.42017}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 5
\pages 759--777
\crossref{https://doi.org/10.1070/sm2000v191n05ABEH000480}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000089654100007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341459}


Linking options:
  • http://mi.mathnet.ru/eng/msb480
  • https://doi.org/10.4213/sm480
  • http://mi.mathnet.ru/eng/msb/v191/i5/p143

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Approximation Properties of the Operators $\mathscr Y_{n+2r}(f)$ and of Their Discrete Analogs”, Math. Notes, 72:5 (2002), 705–732  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. I. I. Sharapudinov, “Mixed series in ultraspherical polynomials and their approximation properties”, Sb. Math., 194:3 (2003), 423–456  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. I. I. Sharapudinov, “Approximation properties of mixed series in terms of Legendre polynomials on the classes $W^r$”, Sb. Math., 197:3 (2006), 433–452  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. I. I. Sharapudinov, “Approximation Properties of the Vallée-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials”, Math. Notes, 84:3 (2008), 417–434  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. I. I. Sharapudinov, G. N. Muratova, “Nekotorye svoistva $r$-kratno integrirovannykh ryadov po sisteme Khaara”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:1 (2009), 68–76  mathnet  elib
    6. 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
    7. 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
    8. 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
    9. 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
    10. 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
    11. 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
    12. I. I. Sharapudinov, T. I. Sharapudinov, “Polynomials, orthogonal on Sobolev, derived by the Chebyshev polynomials, orthogonal on the uniform net”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 5, 56–75  mathnet  crossref
    13. I. I. Sharapudinov, “Asimptoticheskie svoistva polinomov, ortogonalnykh po Sobolevu, porozhdennykh polinomami Yakobi”, Dagestanskie elektronnye matematicheskie izvestiya, 2016, no. 6, 1–24  mathnet  crossref  elib
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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  scopus  scopus
    20. 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
    21. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:307
    Full text:108
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019