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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 780–787 (Mi mz8607)  
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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