The improper infinite derivatives of Takagi's nowhere-differentiable function

Details The improper infinite derivatives of Takagi's nowhere-differentiable function The improper infinite derivatives of Takagi's nowhere-differentiable function

2010-02-13

arxiv.org/abs/1002.2731v1

J. Math. Anal. Appl. 372 (2010) 656-665

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono, we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T'(x) is infinite have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.

Affiliated with

Also associated with

No associations

Rating

The improper infinite derivatives of Takagi's nowhere-differentiable function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The improper infinite derivatives of Takagi's nowhere-differentiable function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The improper infinite derivatives of Takagi's nowhere-differentiable function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-554894