Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find




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

Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 139, Pages 104–113 (Mi into228)  
This article is cited in 4 scientific papers (total in 4 papers)

On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions

I. A. Shakirov

Naberezhnochelninskii State Pedagogical Institute
Full-text PDF (194 kB) Citations (4)
Abstract: The Lebesgue constant corresponding to the classical Fourier operator is approximated by a family of logarithmic functions depending on two parameters. We find optimal values of parameters for which the best uniform approximation of the Lebesgue constant by the specific function of this family is achieved. The case where the corresponding remainder is strictly increasing is also considered.
Keywords: partial sums of Fourier series, norm Fourier operator, Lebesgue constant, asymptotic formula, estimation of Lebesgue constant extremum problem.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 3, Pages 354–363
DOI: https://doi.org/10.1007/s10958-019-04429-0
Bibliographic databases:
Document Type: Article
UDC: 591.65
MSC: 42A20, 57Q55
Language: Russian
Citation: I. A. Shakirov, “On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139, VINITI, M., 2017, 104–113; Journal of Mathematical Sciences, 241:3 (2019), 354–363
Citation in format AMSBIB
\Bibitem{Sha17}
\by I.~A.~Shakirov
\paper On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 139
\pages 104--113
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into228}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799910}
\zmath{https://zbmath.org/?q=an:1428.42004}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 3
\pages 354--363
\crossref{https://doi.org/10.1007/s10958-019-04429-0}
Linking options:
  • https://www.mathnet.ru/eng/into228
  • https://www.mathnet.ru/eng/into/v139/p104
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024