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Izvestiya: Mathematics, 2020, Volume 84, Issue 3, Pages 608–624
DOI: https://doi.org/10.1070/IM8905 (Mi im8905) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series

R. M. Trigub
English version PDF (490 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM8905
Abstract: We establish an asymptotic formula for the rate of approximation of Fourier series of individual periodic functions by linear averages with an error $\omega_{2m}(f;{1}/{n})$, $m\in\mathbb{N}$. This formula is applicable to the means of Riesz, Gauss–Weierstrass, Picard and others. The result is new even for the arithmetic means of partial Fourier sums. We use the formula to determine the asymptotic behaviour of functions in a certain class. Separately, we consider the case of positive integral convolution operators.
Keywords: Fourier series, Wiener algebra of Fourier transforms, comparison principle, modulus of smoothness $\omega_m(f;h)$, positive definite functions, Bernstein's and Schoenberg's theorems.
Received: 13.02.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 3, Pages 185–202
DOI: https://doi.org/10.4213/im8905
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.518.5
MSC: 42A10, 42A16, 42A45, 42A82
Language: English
Original paper language: Russian
Citation: R. M. Trigub, “Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series”, Izv. RAN. Ser. Mat., 84:3 (2020), 185–202; Izv. Math., 84:3 (2020), 608–624
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:596
    Russian version PDF:105
    English version PDF:23
    References:78
    First page:33
     
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