Geodesic
Uniform Convergence of Sine Series with Fractional-Monotone Coefficients
Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 339-346.

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

We study how the well-known criterion for the uniform convergence of a sine series with monotone coefficients changes if, instead of monotonicity, one imposes the condition of $\alpha$-monotonicity with $0\alpha 1$. Moreover, we obtain an addition to the well-known Kolmogorov theorem on the integrability of the sum of a cosine series with convex coefficients tending to zero.
Keywords: trigonometric series, Cesaro numbers.
Mots-clés : uniform convergence 
@article{MZM_2023_114_3_a1,
     author = {M. I. Dyachenko},
     title = {Uniform {Convergence} of {Sine} {Series} with {Fractional-Monotone} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {339--346},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/}
}
TY  - JOUR
AU  - M. I. Dyachenko
TI  - Uniform Convergence of Sine Series with Fractional-Monotone Coefficients
JO  - Matematičeskie zametki
PY  - 2023
SP  - 339
EP  - 346
VL  - 114
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/
LA  - ru
ID  - MZM_2023_114_3_a1
ER  - 
%0 Journal Article
%A M. I. Dyachenko
%T Uniform Convergence of Sine Series with Fractional-Monotone Coefficients
%J Matematičeskie zametki
%D 2023
%P 339-346
%V 114
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/
%G ru
%F MZM_2023_114_3_a1
M. I. Dyachenko. Uniform Convergence of Sine Series with Fractional-Monotone Coefficients. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 339-346. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a1/

[1] E. D. Alferova, A. Yu. Popov, “O polozhitelnosti srednikh summ ryadov po sinusam s monotonnymi koeffitsientami”, Matem. zametki, 110:4 (2021), 630–634 | DOI | MR

[2] A. Yu. Popov, “Utochnenie otsenok summ sinus-ryadov s monotonnymi i kosinus-ryadov s vypuklymi koeffitsientami”, Matem. zametki, 109:5 (2021), 768–780 | DOI

[3] A. Yu. Popov, A. P. Solodov, “Optimalnye na otrezke $[\pi/2,\pi]$ dvustoronnie otsenki summy sinus-ryada s vypukloi posledovatelnostyu koeffitsientov”, Matem. zametki, 112:2 (2022), 317–320 | DOI

[4] T. W. Chaundy, A. E. Jolliffe, “The uniform convergence of a certain class of trigonometric series”, Proc. London Math. Soc. (2), 15 (1916), 214–216 | MR

[5] S. Yu. Tikhonov, “O ravnomernoi skhodimosti trigonometricheskikh ryadov”, Matem. zametki, 81:2 (2007), 304–310 | DOI | MR | Zbl

[6] A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, “Funktsii s obobschenno monotonnymi koeffitsientami Fure”, UMN, 76:6 (462) (2021), 3–70 | DOI | MR | Zbl

[7] A. Zigmund, Trigonometricheskie ryady, T. 1, Mir, M., 1965 | MR

[8] M.I. Dyachenko, “Trigonometricheskie ryady s obobschenno-monotonnymi koeffitsientami”, Izv. vuzov. Matem., 1986, no. 7, 39–50 | MR | Zbl

[9] A. N. Kolmogoroff, “Sur l'ordre de grandeur des coefficients de la serie de Fourier–Lebesgue”, Bull. Acad. Polon., 1923, 83–86

[10] L. A. Balashov, S. A. Telyakovskii, “Nekotorye svoistva lakunarnykh ryadov i integriruemost trigonometricheskikh ryadov”, Analiticheskaya teoriya chisel, matematicheskii analiz i ikh prilozheniya, Sbornik statei. Posvyaschaetsya akademiku Ivanu Matveevichu Vinogradovu k ego vosmidesyatipyatiletiyu, Tr. MIAN SSSR, 143, 1977, 32–41 | MR | Zbl

[11] A. F. Andersen, “Comparison theorems in the theory of Cesaro summability”, Proc. London Math. Soc. (2), 27:1 (1927), 39–71 | MR

[12] E. D. Alferova, M. I. Dyachenko, “$\alpha$-monotonnye posledovatelnosti i teorema Lorentsa”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2023, no. 2, 63–67 | DOI