Fourier Coefficients of Positive Functions.
R. Askey, R.P. jr. Boas (1967)
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R. Askey, R.P. jr. Boas (1967)
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Constantine Georgakis (1973)
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Roop Narain (1958)
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Thomas M. MacRobert (1961)
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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.
M. Mathias (1923)
Mathematische Zeitschrift
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J. J. Duistermaat (1973)
Recherche Coopérative sur Programme n°25
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