Geodesic
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

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An estimate of the convergence rate is obtained in the Riemann localization principle for trigonometric series.
Keywords: Fourier series, Riemann localization principle. 
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/
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[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