Unbounded translation invariant operators on locally compact abelian groups
Let \(T : D(T) \subseteq L_p (G) \to L_p (G)\) be a densely defined linear operator. \(T\) is called translation invariant if and only if \(T\) is closable and commutes with translations. The author characterizes translation invariant operators on \(L_1 (G)\) and \(L_2 (G)\), where \(G\) is a locally compact abelian group. Also, he considers their relationship to translation invariant operators on \(L_p (G)\)-spaces.
scientific article; zbMATH DE number 811182