Publication: Algebrability of the set of non-convergent Fourier series
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2006
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Polish Acad Sciencies Inst Mathematics
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Abstract
We show that, given a set E subset of T of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t is an element of 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.