Geodesic
Approximation of the Lebesgue constant of the Fourier operator by a logarithmic-fractional-rational function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 75-85

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The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (non-monotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.
Mots-clés : Lebesgue constant of the Fourier operator, two-way estimation of the Lebesgue constant
Keywords: fractional rational function, asymptotic formula, extreme problem, approximation error. 
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     author = {I. A. Shakirov},
     title = {Approximation of the {Lebesgue} constant of the {Fourier} operator by a logarithmic-fractional-rational function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--85},
     publisher = {mathdoc},
     number = {11},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_11_a5/}
}
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I. A. Shakirov. Approximation of the Lebesgue constant of the Fourier operator by a logarithmic-fractional-rational function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2023), pp. 75-85. http://geodesic.mathdoc.fr/item/IVM_2023_11_a5/