An "Analytic" Version of Menshov's Representation Theorem
Gady Kozma, Alexander Olevskii
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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