Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izvestiya: Mathematics, 2018, Volume 82, Issue 1, Pages 212–244
DOI: https://doi.org/10.1070/IM8536
(Mi im8536)
 

This article is cited in 26 scientific papers (total in 26 papers)

Sobolev-orthogonal systems of functions associated with an orthogonal system

I. I. Sharapudinovab

a Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala
b Vladikavkaz Scientific Centre of the Russian Academy of Sciences
References:
Abstract: For every system of functions $\{\varphi_k(x)\}$ which is orthonormal on $(a,b)$ with weight $\rho(x)$ and every positive integer $r$ we construct a new associated system of functions $\{\varphi_{r,k}(x)\}_{k=0}^\infty$ which is orthonormal with respect to a Sobolev-type inner product of the form
$$ \langle f,g \rangle=\sum_{\nu=0}^{r-1}f^{(\nu)}(a)g^{(\nu)}(a)+ \int_{a}^{b} f^{(r)}(t)g^{(r)}(t)\rho(t) \,dt. $$
We study the convergence of Fourier series in the systems $\{\varphi_{r,k}(x)\}_{k=0}^\infty$. In the important particular cases of such systems generated by the Haar functions and the Chebyshev polynomials $T_n(x)=\cos(n\arccos x)$, we obtain explicit representations for the $\varphi_{r,k}(x)$ that can be used to study their asymptotic properties as $k\to\infty$ and the approximation properties of Fourier sums in the system $\{\varphi_{r,k}(x)\}_{k=0}^\infty$. Special attention is paid to the study of approximation properties of Fourier series in systems of type $\{\varphi_{r,k}(x)\}_{k=0}^\infty$ generated by Haar functions and Chebyshev polynomials.
Keywords: Sobolev-orthogonal systems of functions associated with Haar functions; Sobolev-orthogonal systems of functions associated with Chebyshev polynomials; convergence of Fourier series of Sobolev-orthogonal functions; approximation properties of partial sums of Fourier series of Sobolev-orthogonal functions; convergence of Fourier series of Sobolev-orthogonal polynomials associated with Chebyshev polynomials.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00486-a
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 16-01-00486-a).
Received: 01.03.2016
Revised: 28.07.2016
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 41A58, 42C10, 33C47
Language: English
Original paper language: Russian
Citation: I. I. Sharapudinov, “Sobolev-orthogonal systems of functions associated with an orthogonal system”, Izv. Math., 82:1 (2018), 212–244
Citation in format AMSBIB
\Bibitem{Sha18}
\by I.~I.~Sharapudinov
\paper Sobolev-orthogonal systems of functions associated with an orthogonal system
\jour Izv. Math.
\yr 2018
\vol 82
\issue 1
\pages 212--244
\mathnet{http://mi.mathnet.ru//eng/im8536}
\crossref{https://doi.org/10.1070/IM8536}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3749601}
\zmath{https://zbmath.org/?q=an:1395.42070}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018IzMat..82..212S}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000427245900008}
\elib{https://elibrary.ru/item.asp?id=32428084}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043697571}
Linking options:
  • https://www.mathnet.ru/eng/im8536
  • https://doi.org/10.1070/IM8536
  • https://www.mathnet.ru/eng/im/v82/i1/p225
  • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:689
    Russian version PDF:80
    English version PDF:31
    References:84
    First page:33
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024