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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
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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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http://mi.mathnet.ru/eng/mz8607https://doi.org/10.4213/mzm8607 http://mi.mathnet.ru/eng/mz/v89/i5/p780
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This publication is cited in the following articles:
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Oniani G., “On Sjolin-Soria-Antonov Type Extrapolation For Locally Compact Groups and a.E. Convergence of Vilenkin-Fourier Series”, Acta Math. Hung.
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