Đề tài " Analytic representation of functions and a new quasianalyticity threshold "

We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere. 1. Introduction . In 1916, D. E. Menshov constructed an example of a nontrivial trigonometric series on the circle T ∞ (1) n=−∞ c(n)eint which converges to zero almost everywhere (.). Such series are called nullseries. This result was the origin of the modern theory of uniqueness in Fourier analysis, see [Z59], [B64], [KL87], [KS94]. Clearly for such a series | c(n)

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2    18    1    27-07-2021