Anti M-Weierstrass function sequences
Functional Analysis
2020-05-29 v2
Abstract
Large algebraic structures are found inside the space of sequences of continuous functions on a compact interval having the property that, the series defined by each sequence converges absolutely and uniformly on the interval but the series of the upper bounds diverges. So showing that there exist many examples satisfying the conclusion but not the hypothesis of the Weierstrass M-test.
Cite
@article{arxiv.2003.10263,
title = {Anti M-Weierstrass function sequences},
author = {M. Carmen Calderón-Moreno and Pablo J. Gerlach-Mena and José A. Prado-Bassas},
journal= {arXiv preprint arXiv:2003.10263},
year = {2020}
}