A characterization of the nowhere differentiable functions of the Generalized Takagi Class

2019/09/12 by Juan Ferrera, Ferrera, Juan, Javier Gómez Gil +3 · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1909.05545

14 pages

arxiv created 2019/09/12 · openalex publication_date 2019/09/12 · arxiv updated 2019/09/13 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that for some Generalized Takagi Classes, in particular for the Takagi-Van der Waerden Class, the functions are nowhere differentiable if, and only if, the sequence of weights does not belong to c₀.

Cited by

• Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions

Related

• Non approximate derivability of the Takagi function
• On the properties of functions of the Takagi power class
• Superdifferential of the Takagi function
• Nonstandard techniques and nowhere differentiable functions I: A dense family of generalized blancmange functions
• The partial derivative of Okamoto's functions with respect to the parameter