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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 780–787 (Mi mz8607)  
This article is cited in 1 scientific paper (total in 1 paper)

Example of a Divergent Fourier Series in the Vilenkin System

I. V. Polyakov

M. V. Lomonosov Moscow State University

Abstract: We construct an example of a function from the class $Lo(\sqrt{\ln^+L})$ whose Fourier–Vilenkin series diverges almost everywhere.

Keywords: Fourier series, Vilenkin system, Walsh system, Vilenkin function, Dirichlet kernel, Rademacher function

DOI: https://doi.org/10.4213/mzm8607

Full text: PDF file (420 kB)
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English version:
Mathematical Notes, 2011, 89:5, 734–740

Bibliographic databases:

UDC: 517.5
Received: 05.11.2009
Revised: 10.11.2010

Citation: I. V. Polyakov, “Example of a Divergent Fourier Series in the Vilenkin System”, Mat. Zametki, 89:5 (2011), 780–787; Math. Notes, 89:5 (2011), 734–740

Citation in format AMSBIB
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\by I.~V.~Polyakov
\paper Example of a Divergent Fourier Series in the Vilenkin System
\jour Mat. Zametki
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\vol 89
\issue 5
\pages 780--787
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\crossref{https://doi.org/10.4213/mzm8607}
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\jour Math. Notes
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\issue 5
\pages 734--740
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Oniani G., “On Sjolin-Soria-Antonov Type Extrapolation For Locally Compact Groups and a.E. Convergence of Vilenkin-Fourier Series”, Acta Math. Hung.  crossref  mathscinet  isi
    		• Математические заметки Mathematical Notes
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