Geodesic
Approximation of the Lebesgue constant of the Fourier operator by a logarithmic function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 86-93

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The Lebesgue constant of the classical Fourier operator is uniformly approximated by a family of logarithmic functions that depend on two parameters. The case where the corresponding residual term has non-monotonic behavior is considered. The obtained result of Lebesgue constant approximation by indicated family of functions strengthens the known results corresponding to cases of strict decrease and increase of the residual term. Various modifications of the logarithmic approximation are studied.
Keywords: Fourier series, asymptotic formula, extreme problem.
Mots-clés : Lebesgue constant of Fourier operator, two-sided Lebesgue constant estimate 
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     author = {I. A. Shakirov},
     title = {Approximation of the {Lebesgue} constant of the {Fourier} operator by a logarithmic function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--93},
     publisher = {mathdoc},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_5_a7/}
}
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I. A. Shakirov. Approximation of the Lebesgue constant of the Fourier operator by a logarithmic function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 86-93. http://geodesic.mathdoc.fr/item/IVM_2022_5_a7/