S. Yu. Tikhonov, “On the Uniform Convergence of Trigonometric Series”, Mat. Zametki, 81:2 (2007), 304–310; Math. Notes, 81:2 (2007), 268

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Matematicheskie Zametki, 2007, Volume 81, Issue 2, Pages 304–310
DOI: https://doi.org/10.4213/mzm3556 (Mi mzm3556)

This article is cited in 20 scientific papers (total in 20 papers)

On the Uniform Convergence of Trigonometric Series

S. Yu. Tikhonov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (388 kB) Citations (20)

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DOI: https://doi.org/10.4213/mzm3556

Abstract: In this paper, we obtain sufficient conditions for the uniform convergence of trigonometric series with monotone (in the extended sense) coefficients.

Keywords: trigonometric series, uniform convergence, monotone (in the extended sense) sequence, lacunary sequence, quasimonotone sequence, Abel transformation.

Received: 28.04.2005
Revised: 09.07.2006

English version:
Mathematical Notes, 2007, Volume 81, Issue 2, Pages 268–274
DOI: https://doi.org/10.1134/S0001434607010294

Bibliographic databases:

UDC: 517.518.4

Language: Russian

Citation: S. Yu. Tikhonov, “On the Uniform Convergence of Trigonometric Series”, Mat. Zametki, 81:2 (2007), 304–310; Math. Notes, 81:2 (2007), 268–274

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Linking options:

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https://doi.org/10.4213/mzm3556

https://www.mathnet.ru/eng/mzm/v81/i2/p304

This publication is cited in the following 20 articles:

M. I. Dyachenko, “Uniform Convergence of Sine Series with Fractional-Monotone Coefficients”, Math. Notes, 114:3 (2023), 296–302
Mateusz Kubiak, Bogdan Szal, “A Sufficient Condition for Uniform Convergence of Trigonometric Series with p-Bounded Variation Coefficients”, Results Math, 78:6 (2023)
A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, “Functions with general monotone Fourier coefficients”, Russian Math. Surveys, 76:6 (2021), 951–1017
Kubiak M., Szal B., “A Necessary Condition For Uniform Convergence of Double Sine Series With P-Bounded Variation Coefficients”, Colloq. Math., 166:2 (2021), 291–312
Lenski W., Singh U., Szal B., “Trigonometric Approximation of Functions in Seminormed Spaces”, Math. Inequal. Appl., 24:1 (2021), 89–101
Karaaslan E., Bagci U., Catbas N., “Attention-Guided Analysis of Infrastructure Damage With Semi-Supervised Deep Learning”, Autom. Constr., 125 (2021), 103634
Kubiak M., Szal B., “Uniform Convergence of Trigonometric Series With P-Bounded Variation Coefficients”, Bull. Belg. Math. Soc.-Simon Steven, 27:1 (2020), 89–110
Duzinkiewicz K., Szal B., “On Weighted Integrability of Double Sine Series”, J. Math. Anal. Appl., 472:2 (2019), 1581–1603
Jose A. Carballo, Javier Bonilla, Manuel Berenguel, Jesús Fernández-Reche, Ginés García, SOLARPACES 2018: International Conference on Concentrating Solar Power and Chemical Energy Systems, 2126, SOLARPACES 2018: International Conference on Concentrating Solar Power and Chemical Energy Systems, 2019, 030012
Duzinkiewicz K., Szal B., “On the Uniform Convergence of Double Sine Series”, Colloq. Math., 151:1 (2018), 71–95
Korus P., “Uniform Convergence of Double Trigonometric Integrals”, Colloq. Math., 154:1 (2018), 107–119
Lenski W., Szal B., “Pointwise Strong Approximation of Almost Periodic Functions in S-1”, Math. Inequal. Appl., 18:2 (2015), 735–750
Lenski W., Szal B., “Applications of General Monotone Sequences to Strong Approximation by Fourier Series”, Indag. Math.-New Ser., 25:1 (2014), 122–130
Lenski W., Szal B., “Strong Approximation of Almost Periodic Functions”, Math. Inequal. Appl., 17:4 (2014), 1353–1364
R. N. Fadeev, “Ravnomernaya skhodimost ryadov po multiplikativnym sistemam”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 13:1(1) (2013), 36–40
S. A. Telyakovskii, “Series formed by the moduli of blocks of terms of trigonometric series. A survey”, J. Math. Sci., 209:1 (2015), 152–158
Szal B., “A New Class of Numerical Sequences and its Applications to Uniform Convergence of Sine Series”, Math. Nachr., 284:14-15 (2011), 1985–2002
Szal B., “Embedding relations connected with strong approximation of Fourier series”, Proc. Indian Acad. Sci. Math. Sci., 120:5 (2010), 563–582
Tikhonov S., “On $L_1$ -convergence of Fourier series”, J. Math. Anal. Appl., 347:2 (2008), 416–427
Tikhonov S., “Best approximation and moduli of smoothness: Computation and equivalence theorems”, J. Approx. Theory, 153:1 (2008), 19–39

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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