This article is cited in 7 papers

Lebesgue constants of the Walsh system and Banach limits

S. V. Astashkin^ab, E. M. Semenov<sup>c

a</sup> 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 $\bigl\{\frac{L_n(W)}{\log_2n},n\ge2\bigr\}$ 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.

UDC: 517.5

Received: 28.05.2015

DOI: 10.17377/smzh.2016.57.303

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

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