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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.

MSC:

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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