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Russian Mathematics

, Volume 63, Issue 9, pp 63–83 | Cite as

Comparison of V- and S-Dini Tests. Counterexamples for Symmetric Dini Tests with Respect to Generalized Haar and Walsh Systems

  • V. I. ShcherbakovEmail author
Article
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Abstract

In this paper, we prove that in symmetric Dini tests with respect to Price and generalized Haar systems both conditions are essential; no one of them alone guarantees the convergence of the Fourier series independently of the majorant of Dirichlet kernels. We give the corresponding counterexamples.

Key words

Abelian group Vilenkin group character systems Price systems generalized Haar systems Dirichlet kernels Dini test 

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Notes

Acknowledgments

The author is grateful to Prof. T.P. Lukashenko for valuable remarks.

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Moscow Technical University of Communications and InformaticsMoscowRussia

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