Geodesic
On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 104-113.

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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, asymptotic formula
Mots-clés : Lebesgue constant, estimation of Lebesgue constant extremum problem. 
@article{INTO_2017_139_a9,
     author = {I. A. Shakirov},
     title = {On optimal approximations of the norm of the {Fourier} operator by a family of logarithmic functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {104--113},
     publisher = {mathdoc},
     volume = {139},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_139_a9/}
}
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I. A. Shakirov. On optimal approximations of the norm of the Fourier operator by a family of logarithmic functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 104-113. http://geodesic.mathdoc.fr/item/INTO_2017_139_a9/