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Sibirsk. Mat. Zh., 2016, Volume 57, Number 3, Pages 512–526 (Mi smj2761)  

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

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 $\{\frac{L_n(W)}{\log_2n},n\ge2\}$ 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).


DOI: https://doi.org/10.17377/smzh.2016.57.303

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English version:
Siberian Mathematical Journal, 2016, 57:3, 398–410

Bibliographic databases:

Document Type: Article
UDC: 517.5
Received: 28.05.2015

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

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