An invitation to the study of evolution equations by means of positive linear operators

This paper provides a detailed survey on a series of methods and results which are centered around the problem of the constructive approximation of the positive semigroups generated by degenerate second order differential operators by means of iterates of positive linear operators. This problem, first states in [7], has been tackled n the last fifteen years from different angles and in different settings such us spaces of bounded and unbounded continuous functions on real intervals as well as on multidimensional convex compact subsets. For the sake of simplicity the presentation is restricted in the framework of compact intervals. The exposition includes several applications as well ad several references for further possible deepening and developments.