2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103725We show that it is possible for a square integrable function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to not belong to the Hardy space. A consequence in the uniqueness theory is obtained.6 pages. Should be identical to journal version except for the French abstractClassical Analysis and ODEsComplex VariablesA null series with small anti-analytic parttext