On the \(C_0\)-semigroups generated by second order differential operators on the real line
The authors consider some classes of (possibly degenerate) elliptic second order differential operators defined on the whole real line and study them in the setting of weighted spaces of continuous functions. Generalizing some results due to Altomare, Attalienti, Campiti, Mangino and Rasa, they first prove that such operators generate strongly continuous semigroups and then they represent them as limits of suitable iterats of integral-type operators. By means of such a representation, some interesting qualitative properties of the semigroups are stated.
scientific article; zbMATH DE number 5568273