Some types of lacunary Fourier series
M. Bożejko, T. Pytlik (1972)
Colloquium Mathematicae
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M. Bożejko, T. Pytlik (1972)
Colloquium Mathematicae
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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.
Jean De Cannière, Ronny Rousseau (1984)
Mathematische Zeitschrift
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