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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 3, Pages 512–526
DOI: https://doi.org/10.17377/smzh.2016.57.303 (Mi smj2761) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Lebesgue constants of the Walsh system and Banach limits

S. V. Astashkinab, E. M. Semenovc

a Samara State University, Samara, Russia
b Samara State Aerospace University, Samara, Russia
c Voronezh State University, Voronezh, Russia
Full-text PDF (499 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2016.57.303
Abstract: We study the properties of the Lebesgue constants of the Walsh system $L_n(W)$, $n\in\mathbb N$, and apply the results to the theory of Banach limits. We show that the sequence $\bigl\{\frac{L_n(W)}{\log_2n},n\ge2\bigr\}$ does not belong to the space of almost convergent sequences ac, which reveals their extremely irregular behavior. Several results of the opposite nature are obtained for some special means of these constants.
Keywords: Walsh functions, Rademacher functions, Lebesgue constants, Banach limit, almost convergent sequence.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 14-01-00141
The first author was supported by the Ministry of Education and Science of the Russian Federation, and the second author was supported by the Russian Foundation for Basic Research (Grant 14-01-00141).
Received: 28.05.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 3, Pages 398–410
DOI: https://doi.org/10.1134/S0037446616030034
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. V. Astashkin, E. M. Semenov, “Lebesgue constants of the Walsh system and Banach limits”, Sibirsk. Mat. Zh., 57:3 (2016), 512–526; Siberian Math. J., 57:3 (2016), 398–410
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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