Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
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



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






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


Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 4, Pages 49–76 (Mi izv2722)  

Pointwise approximation of periodic functions by trigonometric polynomials with Hermitian interpolation

R. M. Trigub

Donetsk National University

Abstract: We prove a general direct theorem on the simultaneous pointwise approximation of smooth periodic functions and their derivatives by trigonometric polynomials and their derivatives with Hermitian interpolation. We study the order of approximation by polynomials whose graphs lie above or below the graph of the function on certain intervals. We prove several inequalities for Hermitian interpolation with absolute constants (for any system of nodes). For the first time we get a theorem on the best-order approximation of functions by polynomials with interpolation at a given system of nodes. We also provide a construction of Hermitian interpolating trigonometric polynomials for periodic functions (in the case of one node, these are trigonometric Taylor polynomials).

Keywords: trigonometric Taylor polynomial, best approximation, modulus of smoothness, two-sided approximation estimates, piecewise one-sided approximation, factorization of differential operators.

DOI: https://doi.org/10.4213/im2722

Full text: PDF file (588 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2009, 73:4, 699–726

Bibliographic databases:

UDC: 517.5
MSC: 41A10, 41A25, 30E10
Received: 30.08.2007

Citation: R. M. Trigub, “Pointwise approximation of periodic functions by trigonometric polynomials with Hermitian interpolation”, Izv. RAN. Ser. Mat., 73:4 (2009), 49–76; Izv. Math., 73:4 (2009), 699–726

Citation in format AMSBIB
\Bibitem{Tri09}
\by R.~M.~Trigub
\paper Pointwise approximation of periodic functions by trigonometric polynomials with Hermitian interpolation
\jour Izv. RAN. Ser. Mat.
\yr 2009
\vol 73
\issue 4
\pages 49--76
\mathnet{http://mi.mathnet.ru/izv2722}
\crossref{https://doi.org/10.4213/im2722}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2583966}
\zmath{https://zbmath.org/?q=an:1180.41007}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2009IzMat..73..699T}
\elib{https://elibrary.ru/item.asp?id=20358689}
\transl
\jour Izv. Math.
\yr 2009
\vol 73
\issue 4
\pages 699--726
\crossref{https://doi.org/10.1070/IM2009v073n04ABEH002463}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000271211200004}
\elib{https://elibrary.ru/item.asp?id=15433899}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-72849150915}


Linking options:
  • http://mi.mathnet.ru/eng/izv2722
  • https://doi.org/10.4213/im2722
  • http://mi.mathnet.ru/eng/izv/v73/i4/p49

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:710
    Full text:155
    References:42
    First page:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021