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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 1, Pages 49–68 (Mi ivm9069)  
This article is cited in 3 scientific papers (total in 3 papers)

Divergence of the Fourier series by generalized Haar systems at points of continuity of a function

V. I. Shcherbakov

Chair of Mathematical Analysis, Moscow Technical University of Communication and Information Science, 32 Narodnogo Opolcheniya str., Moscow, 123995 Russia
Full-text PDF (293 kB) Citations (3)
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Abstract: We obtain a connection between the Dirichlet kernels and partial Fourier sums by generalized Haar and Walsh (Price) systems. Based on this, we establish an interrelation between convergence of the Fourier series by generalized Haar and Walsh (Price) systems. For any unbounded sequence we construct a model of continuous function on a group (and even on a segment $[0,1]$), whose Fourier series by generalized Haar system generated by this sequence, diverges at some point.
Keywords: Abelian group, modified segment $[0,1]$, continuity on modified segment $[0,1]$, systems of characters, Price's systems, generalized Haar's systems.
Received: 26.05.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 1, Pages 42–59
DOI: https://doi.org/10.3103/S1066369X16010059
Bibliographic databases:
Document Type: Article
UDC: 517.52
Language: Russian
Citation: V. I. Shcherbakov, “Divergence of the Fourier series by generalized Haar systems at points of continuity of a function”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 1, 49–68; Russian Math. (Iz. VUZ), 60:1 (2016), 42–59
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/ivm/y2016/i1/p49
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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