A characterization of the nowhere differentiable functions in the Generalized Takagi class

被引：0

作者：

Ferrera, Juan ^{[1
]}

Gómez Gil, Javier ^{[2
]}

Llorente, Jesús ^{[1
]}

机构：

[1] IMI, Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense, Madrid,28040, Spain

[2] Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense, Madrid,28040, Spain

来源：

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas | 2025年 / 119卷 / 01期

关键词：

The Takagi function; Generalized Takagi class; Nowhere differentiable functions; Fréchet subdifferential; Primary 26A27; 26A30; 26A24;

D O I：

10.1007/s13398-024-01673-1

中图分类号：

学科分类号：

摘要：

In this paper, we explore the non-differentiability behavior of the functions belonging to the Generalized Takagi class, a recent generalization of the Takagi function. It is derived by replacing the dyadic numbers used in the definition of classical Takagi function with an arbitrary countable and dense subset of [0, 1]. Subject to specific conditions on the decomposition of such a set, we demonstrate that a function within this class is nowhere differentiable if and only if the sequence of weights does not belong to c0. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2024.

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