Ensembles de non synthèse pour certains poids dissymétriques sur la droite
Volume 104 / 1993
Studia Mathematica 104 (1993), 1-12
DOI: 10.4064/sm-104-1-1-12
Abstract
Let w be a weight and let $L^1(ℝ,w)$ be the algebra of all measurable functions f on ℝ such that fw is integrable. It is known that if S is a closed countable subset of ℝ then S satisfies the spectral synthesis in $L^1(ℝ, w)$ for all weights w such that ${w(t) = 1 for t ≥ 0, lim sup_{t→∞} (Logw(-t))/(t^{1/2}) = 0$. We prove here that this result fails for a large class of uncountable closed subsets of ℝ with Lebesgue measure zero.
