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Uniform Convergence of Trigonometric Series with General Monotone Coefficients

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 January 2019

Mikhail Dyachenko ,
Askhat Mukanov  and
Sergey Tikhonov
Mikhail Dyachenko
Affiliation:
Department of Mechanics and Mathematics, Lomonosov Moscow State University, MSU, GSP-1, Moscow, 119991, Russia Email: dyach@mail.ru
Askhat Mukanov
Affiliation:
Centre de Recerca Matemàtica and Universitat Autónoma de Barcelona, Departament de Matematiques, Edifici C Facultat de Ciències, 08193 Bellaterra (Barcelona), Spain Kazakhstan Branch of Lomonosov Moscow State University, Kazhymukan St., 11, Astana, 010010, Kazakhstan Email: mukanov.askhat@gmail.com
Sergey Tikhonov
Affiliation:
Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C 08193 Bellaterra (Barcelona), Spain ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain, and Universitat Autónoma de Barcelona Email: stikhonov@crm.cat
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Abstract

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We study criteria for the uniform convergence of trigonometric series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such series.

Keywords

trigonometric seriesgeneral monotone sequenceuniform convergence

MSC classification

Primary: 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series
Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 6 , December 2019 , pp. 1445 - 1463
Copyright
© Canadian Mathematical Society 2018 

Footnotes

This research was partially supported by RFFI no. 16-01-00350, MTM 2014-59174-P, 2014 SGR 289, the grants of Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (projects AP05131707, AP05133301), and by the CERCA Programme of the Generalitat de Catalunya.

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