Analytic representation of functions and a new quasi-analyticity threshold. (English) Zbl 1215.42012

Summary: We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere.


42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A50 Conjugate functions, conjugate series, singular integrals
30B30 Boundary behavior of power series in one complex variable; over-convergence
42A61 Probabilistic methods for one variable harmonic analysis
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