Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth
Classical Analysis and ODEs
2016-10-21 v1
Abstract
Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier transformation, the method consists in principle of a second microlocalisation, which is used to derive two general results on existence of nowhere differentiable functions. Examples are given in which the frequencies are of polynomial growth and of almost quadratic growth as a borderline case.
Keywords
Cite
@article{arxiv.1610.06354,
title = {Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth},
author = {Jon Johnsen},
journal= {arXiv preprint arXiv:1610.06354},
year = {2016}
}
Comments
16 pages. Update of the accepted version, with correction of a few misprints, including "liminf" instead of "limsup" in line 2-3 after formula (2.2). (The final publication is available at Springer via http://dx.doi.org/10.1007/s00041-009-9072-2)