Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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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}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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