An "Analytic" Version of Menshov's Representation Theorem
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/0512003,
title = {An "Analytic" Version of Menshov's Representation Theorem},
author = {Gady Kozma and Alexander Olevskii},
journal= {arXiv preprint arXiv:math/0512003},
year = {2007}
}
Comments
4 pages. Announcement of math.CA/0510616. Should be identical to journal version except for the French abstract