Pieter C. Allaart
Published 2013-01-21, updated 2013-10-17Version 2
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.
Comments: 34 pages, 5 figures. The statement of Theorem 1.1 was expanded and various improvements to the presentation were made
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