Convolution functions that are nowhere differentiable

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Jimenez-Rodriguez, P.¹  Maghsoudi, S.²  Munoz-Fernandez, G. A.¹ 

[1] Univ Complutense Madrid, Dept Anal Matemat, Fac Ciencias Matemat, Plaza Ciencias 3, E-28040 Madrid, Spain

[2] Univ Zanjan, Dept Math, Zanjan 45195313, Iran

关键词: Lineability;    Spaceability;    Algebrability;    Convolution;    Nowhere differentiable function;   

DOI  :  10.1016/j.jmaa.2013.12.008

来源: Elsevier

【 摘 要 】

In 1951 V. Jarnik constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarnik's results by proving that the set of such functions is maximal lineable. This would shed some light on a question posed in 1973 on the structure of the set of continuous functions whose Volterra convolution is nowhere differentiable. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free