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An "Analytic" Version of Menshov's Representation Theorem

Gady Kozma·Alexander Olevskii
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Abstract

Every measurable function f on the circle can be represented as a sum of harmonics with positive spectrum, converging in measure. For convergence almost everywhere this is not true. We discuss several other subsets of Z for which one might get a Menshov type representation converging almost everywhere or in measure.

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Gady Kozma, Alexander Olevskii. 2005-12-01. An "Analytic" Version of Menshov's Representation Theorem. https://doi.org/10.1016/s0764-4442(00)01616-5

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