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Lebesgue constants of the Walsh system and Banach limits

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Abstract

We study the properties of the Lebesgue constants of the Walsh system L n (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.

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Authors and Affiliations

  1. Samara State University, Samara State Aerospace University, Samara, Russia

    S. V. Astashkin

  2. Voronezh State University, Voronezh, Russia

    E. M. Semenov

Authors
  1. S. V. Astashkin
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  2. E. M. Semenov
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Correspondence to S. V. Astashkin.

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Samara; Voronezh. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 3, pp. 512–526, May–June, 2016; DOI: 10.17377/smzh.2016.57.303.

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Astashkin, S.V., Semenov, E.M. Lebesgue constants of the Walsh system and Banach limits. Sib Math J 57, 398–410 (2016). https://doi.org/10.1134/S0037446616030034

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  • DOI: https://doi.org/10.1134/S0037446616030034

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