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

Abstract

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