Estimate of the convergence rate in the Riemann localization principle for trigonometric Fourier series of continuous functions
Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 290-305.

Voir la notice de l'article provenant de la source Math-Net.Ru

An estimate of the convergence rate is obtained in the Riemann localization principle for trigonometric series.
Keywords: Fourier series, Riemann localization principle.
@article{MZM_2024_116_2_a9,
     author = {T. Yu. Semenova},
     title = {Estimate of the convergence rate in the {Riemann} localization principle for trigonometric {Fourier} series of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {290--305},
     publisher = {mathdoc},
     volume = {116},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a9/}
}
TY  - JOUR
AU  - T. Yu. Semenova
TI  - Estimate of the convergence rate in the Riemann localization principle for trigonometric Fourier series of continuous functions
JO  - Matematičeskie zametki
PY  - 2024
SP  - 290
EP  - 305
VL  - 116
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a9/
LA  - ru
ID  - MZM_2024_116_2_a9
ER  - 
%0 Journal Article
%A T. Yu. Semenova
%T Estimate of the convergence rate in the Riemann localization principle for trigonometric Fourier series of continuous functions
%J Matematičeskie zametki
%D 2024
%P 290-305
%V 116
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a9/
%G ru
%F MZM_2024_116_2_a9
T. Yu. Semenova. Estimate of the convergence rate in the Riemann localization principle for trigonometric Fourier series of continuous functions. Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 290-305. http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a9/

[1] E. Hille, G. Klein, “Riemann's localization theorem for Fourier series”, Duke Math. J., 21 (1954), 587–591 | DOI | MR

[2] S. A. Telyakovskii, “Printsip lokalizatsii Rimana, otsenka skorosti skhodimosti”, Teoriya funktsii, SMFN, 25, RUDN, M., 2007, 178–181 | MR

[3] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[4] V. T. Gavrilyuk, S. B. Stechkin, “Priblizhenie nepreryvnykh periodicheskikh funktsii summami Fure”, Issledovaniya po teorii funktsii mnogikh deistvitelnykh peremennykh i priblizheniyu funktsii, Sbornik statei, Tr. MIAN SSSR, 172, 1985, 107–127 | MR | Zbl

[5] I. A. Shakirov, “About the optimal replacement of the Lebesgue constant Fourier operator by a logarithmic function”, Lobachevskii J. Math., 39:6 (2018), 841–846 | DOI | MR

[6] A. Yu. Popov, T. Yu. Semenova, “Utochnenie otsenki skorosti ravnomernoi skhodimosti ryada Fure nepreryvnoi periodicheskoi funktsii ogranichennoi variatsii”, Matem. zametki, 113:4 (2023), 544–559 | DOI | MR