Hausdorff dimension of level sets of generalized Takagi functions
Classical Analysis and ODEs
2019-02-20 v2
Abstract
This paper examines level sets of two families of continuous, nowhere differentiable functions (one a subfamily of the other) defined in terms of the "tent map". The well-known Takagi function is a special case. Sharp upper bounds are given for the Hausdorff dimension of the level sets of functions in these two families. Furthermore, the case where a function f is chosen at random from either family is considered, and results are given for the Hausdorff dimension of the zero set and the set of maximum points of f.
Keywords
Cite
@article{arxiv.1301.4747,
title = {Hausdorff dimension of level sets of generalized Takagi functions},
author = {Pieter C. Allaart},
journal= {arXiv preprint arXiv:1301.4747},
year = {2019}
}
Comments
34 pages, 5 figures. The statement of Theorem 1.1 was expanded and various improvements to the presentation were made