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Series with monotone coefficients by Walsh system

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Abstract

The paper studies the series \(\sum\limits_{n = 0}^\infty {a_n } W_n (x)\) by Walsh system, where |a n | monotone tends to zero and \(\sum\limits_{n = 1}^\infty {a_{_n }^2 } = \infty \). Some theorems on correction in L 1 and representability of functions from L p, p ∈ (0, 1) by subseries of the Walsh series are proved.

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Authors and Affiliations

  1. Yerevan State University, Russia

    K. A. Navasardyan

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  1. K. A. Navasardyan
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Correspondence to K. A. Navasardyan.

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Original Russian Text © K. A. Navasardyan, 2007, published in Izvestiya NAN Armenii. Matematika, 2007, No. 5, pp. 26–41.

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Navasardyan, K.A. Series with monotone coefficients by Walsh system. J. Contemp. Mathemat. Anal. 42, 258–269 (2007). https://doi.org/10.3103/S1068362307050032

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  • DOI: https://doi.org/10.3103/S1068362307050032

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