RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2017, Volume 101, Issue 4, Pages 611–629 (Mi mz10987)  

This article is cited in 3 scientific papers (total in 3 papers)

Approximation Properties of Fourier Series of Sobolev Orthogonal Polynomials with Jacobi Weight and Discrete Masses

I. I. Sharapudinovab

a Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala
b Daghestan State Pedagogical University

Abstract: We study Fourier series of Jacobi polynomials $P_k^{\alpha-r,-r}(x)$, $k=r,r+1,…$, orthogonal with respect to the Sobolev-type inner product of the following form:
$$ \langle f,g\rangle=\sum_{\nu=0}^{r-1} f^{(\nu)}(-1)g^{(\nu)}(-1) +\int_{-1}^1f^{(r)}(t)g^{(r)}(t)(1-t)^\alpha dt. $$
It is shown that such series are a particular case of mixed series of Jacobi polynomials $P_k^{\alpha,\beta}(x)$, $k=0,1,…$, considered earlier by the author. We study the convergence of mixed series of general Jacobi polynomials and their approximation properties. The results obtained are applied to the study of the approximation properties of Fourier series of Sobolev orthogonal Jacobi polynomials $P_k^{\alpha-r,-r}(x)$.

Keywords: mixed series of Sobolev orthogonal Jacobi polynomials Jacobi polynomials, Fourier–Sobolev series of Jacobi polynomials and their approximation properties.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00486
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00486.


DOI: https://doi.org/10.4213/mzm10987

Full text: PDF file (609 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2017, 101:4, 718–734

Bibliographic databases:

UDC: 517.538
Received: 15.10.2015
Revised: 30.04.2016

Citation: I. I. Sharapudinov, “Approximation Properties of Fourier Series of Sobolev Orthogonal Polynomials with Jacobi Weight and Discrete Masses”, Mat. Zametki, 101:4 (2017), 611–629; Math. Notes, 101:4 (2017), 718–734

Citation in format AMSBIB
\Bibitem{Sha17}
\by I.~I.~Sharapudinov
\paper Approximation Properties of Fourier Series of Sobolev Orthogonal Polynomials with Jacobi Weight and Discrete Masses
\jour Mat. Zametki
\yr 2017
\vol 101
\issue 4
\pages 611--629
\mathnet{http://mi.mathnet.ru/mz10987}
\crossref{https://doi.org/10.4213/mzm10987}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3629050}
\elib{http://elibrary.ru/item.asp?id=28931422}
\transl
\jour Math. Notes
\yr 2017
\vol 101
\issue 4
\pages 718--734
\crossref{https://doi.org/10.1134/S0001434617030300}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000401454600030}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018828482}


Linking options:
  • http://mi.mathnet.ru/eng/mz10987
  • https://doi.org/10.4213/mzm10987
  • http://mi.mathnet.ru/eng/mz/v101/i4/p611

    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, M. G. Magomed-Kasumov, “Chislennyi metod resheniya zadachi Koshi dlya sistem obyknovennykh differentsialnykh uravnenii s pomoschyu ortogonalnoi v smysle Soboleva sistemy, porozhdennoi sistemoi kosinusov”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 53–60  mathnet  crossref
    2. M. G. Magomed-Kasumov, “Sistema funktsii, ortogonalnaya v smysle Soboleva i porozhdennaya sistemoi Uolsha”, Matem. zametki, 105:4 (2019), 545–552  mathnet  crossref  elib
    3. R. M. Gadzhimirzaev, “Sobolev-orthonormal system of functions generated by the system of Laguerre functions”, Probl. anal. Issues Anal., 8(26):1 (2019), 32–46  mathnet  crossref
  • Математические заметки Mathematical Notes
    Number of views:
    This page:255
    References:39
    First page:28

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