The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem

Raymond Mortini

Abstract


Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's  theorem the  Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.

Keywords


Boundary behaviour of analytic functions; trigonometric series

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References


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Lusin, N., Privaloff, J., Sur l’unicite et la multiplicite des fonctions analytiques, Ann. Sci. ENS 42 (1925), 143-191.

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DOI: http://dx.doi.org/10.17951/a.2017.71.1.73
Date of publication: 2017-06-30 17:33:57
Date of submission: 2017-06-30 13:18:07


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