2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106038Every 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.4 pages. Announcement of math.CA/0510616. Should be identical to journal version except for the French abstractClassical Analysis and ODEsComplex Variablestext