Algebraic genericity and the differentiability of the convolution

JOURNAL OF APPROXIMATION THEORY

卷:241

Article

Jimenez-Rodriguez, P.¹  Munoz-Fernandez, G. A.²  Saez-Maestro, E.³  Seoane-Sepulveda, J. B.² 

[1] Dept Math Sci, Math & Comp Sci Bldg,Summit St, Kent, OH 44242 USA

[2] Univ Complutense Madrid, Fac Ciencias Matemat, IMI, Plaza Ciencias 3, E-28040 Madrid, Spain

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

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

DOI  :  10.1016/j.jat.2019.01.002

来源: Elsevier

【 摘 要 】

Despite the convolution preserving most of the smooth properties of the functions that take part in it, there exist differentiable functions whose convolution is not differentiable. In the present result, we study the algebraic genericity of the set of those functions. In particular, it is proved that periodic continuous functions can be approximated by functions belonging to a vector space each of whose nonzero members generates some convolution which is not differentiable. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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