RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Uspekhi Mat. Nauk, 1974, Volume 29, Issue 3(177), Pages 9–42 (Mi umn4374)  

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

On extremal problems in the theory of best approximation

N. P. Korneichuk


Abstract: This article is of the nature of a survey. It sets out the basic steps of the investigations into the exact solution of extremal problems in the theory of approximation for classes of periodic functions in their historical aspect (best approximation by trigonometric polynomials, diameters, approximation of one class of functions by another, etc.) Special attention is given to explaining the principles characterizing the various approaches to the solution of the problems. A method worked out by the author and connected with the application of a special operator that is defined by means of rearrangements is expounded in greater detail. This method enables us to obtain an exact solution of certain extremal problems for the classes $W^rH^\omega$.

Full text: PDF file (1759 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1974, 29:3, 7–43

Bibliographic databases:

UDC: 517.5
MSC: 42A05, 41A50, 41A10, 41A30
Received: 18.02.1974

Citation: N. P. Korneichuk, “On extremal problems in the theory of best approximation”, Uspekhi Mat. Nauk, 29:3(177) (1974), 9–42; Russian Math. Surveys, 29:3 (1974), 7–43

Citation in format AMSBIB
\Bibitem{Kor74}
\by N.~P.~Korneichuk
\paper On extremal problems in the theory of best approximation
\jour Uspekhi Mat. Nauk
\yr 1974
\vol 29
\issue 3(177)
\pages 9--42
\mathnet{http://mi.mathnet.ru/umn4374}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402360}
\zmath{https://zbmath.org/?q=an:0366.41011|0373.41026}
\transl
\jour Russian Math. Surveys
\yr 1974
\vol 29
\issue 3
\pages 7--43
\crossref{https://doi.org/10.1070/RM1974v029n03ABEH001284}


Linking options:
  • http://mi.mathnet.ru/eng/umn4374
  • http://mi.mathnet.ru/eng/umn/v29/i3/p9

    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. Wolfgang Dahmen, “Trigonometric approximation with exponential error orders”, Math Ann, 230:1 (1977), 57  crossref  mathscinet  zmath
    2. Stephen D Fisher, “Best approximation by polynomials”, Journal of Approximation Theory, 21:1 (1977), 43  crossref
    3. Herbert F. Sinwel, “Uniform approximation of differentiable functions by algebraic polynomials”, Journal of Approximation Theory, 32:1 (1981), 1  crossref
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:433
    Full text:205
    References:69
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020