Jesús Llorente: Nonsmooth analysis of the Takagi-Van der Waerden functions

ELTE Analízis tanszék szemináruma

Abstract: Takagi-Van der Waerden functions are an immediate generalization of the Takagi function and they constitute a family of continuous nowhere differentiable functions. In this talk, we will investigate the non-differentiability behavior of the Takagi-Van der Waerden functions from two different approaches.

On the one hand, we will characterize the sets of points where they have an infinite derivative. On the other hand, we will completely describe the superdifferential of the Takagi-Van der Waerden functions. In addition, the Hausdorff dimension and the corresponding Hausdorff measure of the set of points where the superdifferential  is not empty will be obtained.