Generalized group algebras and generalized measure algebras on non-discrete locally compact abelian groups

Jyunji Inoue, Sin-Ei Takahasi

Let $G$ be a non-discrete LCA group with the dual group $\Gamma$. We define generalized group algebra, ${\mathcal{L}}^1(G)$, and generalized measure algebra, $\mathcal{M}(G),$ on $G$ as…