Algebrability of the set of non-convergent Fourier series
Volume 175 / 2006
Studia Mathematica 175 (2006), 83-90
MSC: Primary 42A20, 46E25; Secondary 42A16.
DOI: 10.4064/sm175-1-5
Abstract
We show that, given a set $E\subset \mathbb T$ of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point $t\in E$ is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of $\mathcal{C}({\mathbb T})$ every non-zero element of which has a Fourier series expansion divergent in $E$.
