Smooth compositions with a nonsmooth inner function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Shi, Yongjie¹  Yu, Chengjie¹ 

[1] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China

关键词: Baire space;    Baire's category theorem;    Periodic function;   

DOI  :  10.1016/j.jmaa.2017.05.028

来源: Elsevier

【 摘 要 】

Let p : R -> R be a given function, and let A(p) be the set of smooth functions f such that f (p(.) + c) is smooth for any c is an element of R. We show that if p is not smooth, then either every element of A(p) is constant, or there is a nonzero constant d such that A(p) is equal to the set of smooth functions of periodicity d. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free