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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 1, Pages 49–68
(Mi ivm9069)
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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
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
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
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https://www.mathnet.ru/eng/ivm9069 https://www.mathnet.ru/eng/ivm/y2016/i1/p49
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Abstract page: | 139 | Full-text PDF : | 41 | References: | 56 | First page: | 37 |
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