无最小正周期的周期函数的构造及其性质

The Construction and Properties of Periodic Function without Minimal Positive Period

从群论的角度给出周期函数的等价定义.对任意给定的非循环群GR),构造出以G为周期集的无最小正周期的周期函数.讨论无最小正周期的周期函数的性质.

An equivalent definition is given from the perspective of group theory. For any given G（G is a subset of R）, which is not a cyclic group, the periodic function with G as periodic set is constructed, and it is without minimal positive period. Properties of periodic function without minimal positive period is discussed.