Beurling-Helson定理的定量形式
Quantitative version of Beurling-Helson theorem
摘要：
证明了单位圆上任意连续函数f，使得序列e^{in f}，n= 1，2，.具有小的Wiener范数e^{in f} A = o（\frac{\log^{1/22} |n|}{(\log \log |n|)^{3/11}}），是线性的.在素数p的情况下，得到了子集Z_p的特征函数的Wiener范数的下界.
英文摘要：
It is proved that any continuous function f on the unit circle such that the sequence e^{in f}, n=1,2,... has small Wiener norm \| e^{in f} \|_A = o (\frac{\log^{1/22} |n|}{(\log \log |n|)^{3/11}}), is linear. Moreover, we get lower bounds for Wiener norm of characteristic functions of subsets from Z_p in the case of prime p.
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