# An "Analytic" Version of Menshov's Representation Theorem

Research paper by Gady Kozma, Alexander Olevskii

Indexed on: 30 Nov '05Published on: 30 Nov '05Published in: Mathematics - Classical Analysis and ODEs

#### 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.