Fejér means for multivariate Fourier series.
Hubert Berens, Yuan Xu (1996)
Mathematische Zeitschrift
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Hubert Berens, Yuan Xu (1996)
Mathematische Zeitschrift
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W. Gautschi (1971/72)
Numerische Mathematik
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M. Mathias (1923)
Mathematische Zeitschrift
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M. Bożejko, T. Pytlik (1972)
Colloquium Mathematicae
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Zhihua Zhang (2017)
Open Mathematics
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Due to discontinuity on the boundary, traditional Fourier approximation does not work efficiently for d−variate functions on [0, 1]d. In this paper, we will give a recursive method to reconstruct/approximate functions on [0, 1]d well. The main process is as follows: We reconstruct a d−variate function by using all of its (d−1)–variate boundary functions and few d–variate Fourier coefficients. We reconstruct each (d−1)–variate boundary function given in the preceding reconstruction by...
Beriša, Muharem C. (1985)
Publications de l'Institut Mathématique. Nouvelle Série
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Zhang, Qing-Hua, Chen, Shuiming, Qu, Yuanyuan (2005)
International Journal of Mathematics and Mathematical Sciences
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John J. F. Fournier (1985)
Colloquium Mathematicae
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(1970)
Czechoslovak Mathematical Journal
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Shiba, Masaaki (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Frank Natterer (1985)
Numerische Mathematik
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Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda (2006)
Studia Mathematica
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We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.