Quantitative version of Beurling-Helson theorem
Abstract
It is proved that any continuous function f on the unit circle such that the sequence ein f, n=1,2,... has small Wiener norm \| ein f \|A = o (1/22 |n|( |n|)3/11), is linear. Moreover, we get lower bounds for Wiener norm of characteristic functions of subsets from Zp in the case of prime p.
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