Algebrability of the set of non-convergent Fourier series

Richard M. Aron, David Pérez-García, and Juan B. Seoane-Sepúlveda. "Algebrability of the set of non-convergent Fourier series." Studia Mathematica 175.1 (2006): 83-90. <http://eudml.org/doc/284956>.

@article{RichardM2006,
abstract = {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.},
author = {Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda},
journal = {Studia Mathematica},
keywords = {Fourier series; divergent series; lineability; spaceability; algebrability},
language = {eng},
number = {1},
pages = {83-90},
title = {Algebrability of the set of non-convergent Fourier series},
url = {http://eudml.org/doc/284956},
volume = {175},
year = {2006},
}

TY - JOUR
AU - Richard M. Aron
AU - David Pérez-García
AU - Juan B. Seoane-Sepúlveda
TI - Algebrability of the set of non-convergent Fourier series
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 1
SP - 83
EP - 90
AB - 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.
LA - eng
KW - Fourier series; divergent series; lineability; spaceability; algebrability
UR - http://eudml.org/doc/284956
ER -