On the BSE and BED properties of the Beurling algebra $L^1(G,ω)$

Abstract

Let $G$ be a locally compact abelian group, and let $ω:G \to [1,\infty)$ be a weight, i.e., $ω$ is measurable, $ω$ is locally bounded and $ω(s+t)\leq ω(s)ω(t)$ for all $s, t \in G$. If $ω^{-1}$ is vanishing at infinity, then we show that the Beurling algebra $L^1(G,ω)$ is both BSE- algebra and BED- algebra.