关于周期函数之和的周期性

On Pcfiodicity of The Sum of Periodic Functions

本文用数学分析的方法，证明了定理；设ｆ（ｘ），ｇ（ｘ）是定义于Ｒ上的周期函数，它们的最小正周期分别为Ｔ１，Ｔ２．如果ｆ（ｘ），ｇ（ｘ）至少有一个是连续的，且Ｔ１，Ｔ２不可公度，则ｆ（ｘ）十ｇ（ｘ）是非周期函数，在某种意义下，这个定理是“最佳可能”的。

The folluwing theurem is pruved:let T1, T2 be two least positive periods of two periodicfunctions f(x)and g(x), respectively, which defined on the real line.If(1) T1 and T2 are non -com-mensurable,(2)one of f(x)and g(x) is a continuous function ,then f(x)+g(x) is aperiodic func-tion. This theorem is optimally possible,in a manner.