This article is cited in 1 paper

Estimates of the Dirichlet Kernel and Divergent Fourier Series in the Walsh–Kaczmarz System

I. V. Polyakov

M. V. Lomonosov Moscow State University

Abstract: A new lower bound for the growth of the Dirichlet kernel for the Walsh–Kaczmarz system is obtained and an example of an almost everywhere divergent Fourier series with respect to this system from a class narrower than that examined earlier is constructed.

Keywords: Dirichlet kernel, Fourier series, Walsh–Kaczmarz system, Kaczmarz indexing, Lebesgue measure, Walsh function.

UDC: 517.5

Received: 31.01.2008
Revised: 15.01.2013

DOI: 10.4213/mzm4509

 English version: Mathematical Notes, 2014, 95:2, 234–246

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