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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 2, Pages 277–292
DOI: https://doi.org/10.17377/smzh.2018.59.204 (Mi smj2971) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness

Sh. A. Balgimbayeva, T. I. Smirnov

Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Full-text PDF (366 kB) Citations (3)
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DOI: https://doi.org/10.17377/smzh.2018.59.204
Abstract: We obtain some order-sharp estimates for the Fourier widths of Nikol'skii–Besov and Lizorkin–Triebel function classes with given majorant of the mixed modulus of smoothness in the Lebesgue space for a few relations between the parameters of the class and the space. The upper bounds follow from estimates of the approximation of functions of these classes by special partial sums of their Fourier series with respect to the multiple system of periodized Meyer wavelets.
Keywords: Fourier width, function space, wavelet system, mixed modulus of smoothness, majorant.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 5130/ГФ4
AP05133257
The authors were supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grants 5130/GF4 and AP05133257).
Received: 29.06.2016
Revised: 10.01.2018
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 2, Pages 217–230
DOI: https://doi.org/10.1134/S0037446618020040
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 35R30
Language: Russian
Citation: Sh. A. Balgimbayeva, T. I. Smirnov, “Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness”, Sibirsk. Mat. Zh., 59:2 (2018), 277–292; Siberian Math. J., 59:2 (2018), 217–230
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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