Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
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

Mathematics of the USSR-Sbornik, 1989, Volume 63, Issue 1, Pages 229–246
DOI: https://doi.org/10.1070/SM1989v063n01ABEH003270 (Mi sm1698) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On approximation of functions by singular integrals in the Hausdorff metric

A. P. Petukhov
English version PDF (751 kB) Citations (3) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM1989v063n01ABEH003270
Abstract: Necessary and sufficient conditions are found for convergence in the Hausdorff metric of a sequence of integral operators on an arbitrary bounded measurable function. The criterion obtained is used to investigate summation of trigonometric Fourier series by the Abel–Poisson, Vallée-Poussin, Bernstein–Rogosinski, and Cesàro methods.
Bibliography: 7 titles.
Received: 06.01.1987
Bibliographic databases:
UDC: 517.5
MSC: Primary 45P05, 45E10, 42B20; Secondary 42A24, 40G05, 40G10
Language: English
Original paper language: Russian
Citation: A. P. Petukhov, “On approximation of functions by singular integrals in the Hausdorff metric”, Math. USSR-Sb., 63:1 (1989), 229–246
Citation in format AMSBIB
\Bibitem{Pet88}
\by A.~P.~Petukhov
\paper On approximation of functions by singular integrals in the Hausdorff metric
\jour Math. USSR-Sb.
\yr 1989
\vol 63
\issue 1
\pages 229--246
\mathnet{http://mi.mathnet.ru/eng/sm1698}
\crossref{https://doi.org/10.1070/SM1989v063n01ABEH003270}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=937809}
\zmath{https://zbmath.org/?q=an:0693.42016}
Linking options:
  • https://www.mathnet.ru/eng/sm1698
  • https://doi.org/10.1070/SM1989v063n01ABEH003270
  • https://www.mathnet.ru/eng/sm/v177/i2/p235
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025