On a class of exponential-type operators and their limit semigroups Original Research Article

The paper is mainly focused upon the study of a class of second order degenerate elliptic operators on unbounded intervals. We show that these operators generate strongly continuous semigroups in suitable weighted spaces of continuous functions. Furthermore, we represent the semigroups as limits of iterates of the so-called exponential-type operators. In a particular case, starting from the stochastic differential equations associated with these operators, we also find an integral representation of the semigroup and determine its asymptotic behaviour.