Abstract

It is known that, among all the differentiable homeomorphic changes of variable, only the functions \(\varphi_1 (x)=x\) and \(\varphi_2 (x)=1-x\), \(x\in[0,1]\), preserve the absolute convergence of Fourier–Haar series everywhere. It is established that the class of all differentiable homeomorphic changes of variable that preserve absolute convergence everywhere will not become wider if we restrict ourselves to continuous external functions.

中文翻译：

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关于保持连续函数傅里叶-哈尔级数绝对收敛的变量的变化

摘要

已知，在变量的所有可微同胚变化中，只有函数\(\varphi_1 (x)=x\)和\(\varphi_2 (x)=1-x\) , \(x\in[0 ,1]\)，保持傅立叶-哈尔级数的绝对收敛性。已经确定，如果我们将自己限制在连续的外部函数上，那么在任何地方都保持绝对收敛的变量的所有可微同胚变化的类别不会变得更宽。