关于Chang-Green-Ruzsa定理的一个注记

A remark on Chang-Green-Ruzsa′s theorem

Green和Ruzsa对Chang定理的证明中没有考虑ρ-谱中分离集出现实特征的情况.首先举例说明分离集和谱中分离集均可以包含实特征,然后通过研究函数Fc,ω的性质,并进行相关计算,得到了Chang定理的校正形式.

In the proof of Chang-Green-Ruzsa s theorem the case of real characters in dissociated set of - spectrum is notstudied. It is illustrated that dissociated set and dissociated set of p- spectrum may contain real characters. The correctionform of the theorem is given by investigating the properties of Fc,ω and correlation calculation.