A continuum dimensional algebra of nowhere differentiable functions
Classical Analysis and ODEs
2023-07-31 v2
Abstract
We construct an algebra of dimension consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions which are differentiable at some points, but where for all functions in the algebra the set of points of differentiability is quite small.
Cite
@article{arxiv.2307.11738,
title = {A continuum dimensional algebra of nowhere differentiable functions},
author = {Jan-Christoph Schlage-Puchta},
journal= {arXiv preprint arXiv:2307.11738},
year = {2023}
}
Comments
Several typos corrected. To appear in Mathematica Pannonica