Email this article Lebesgue constants of the Walsh system and Banach limits
- Authors: Astashkin S.V.1, Semenov E.M.2
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Affiliations:
- Samara State University
- Voronezh State University
- Issue: Vol 57, No 3 (2016)
- Pages: 398-410
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170444
- DOI: https://doi.org/10.1134/S0037446616030034
- ID: 170444
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Abstract
We study the properties of the Lebesgue constants of the Walsh system Ln(W), n ∈ N, and apply the results to the theory of Banach limits. We show that the sequence \(\left\{ {\frac{{{L_n}\left( W \right)}}{{{{\log }_2}n}},n \geqslant 2} \right\}\) 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.
About the authors
S. V. Astashkin
Samara State University
Author for correspondence.
Email: astash@samsu.ru
Russian Federation, Samara
E. M. Semenov
Voronezh State University
Email: astash@samsu.ru
Russian Federation, Voronezh
