A Class of Ordinary Differential Operators on a Half Line

Abstract

Ordinary differential operators on a half line differ considerably from their counterparts on a finite interval. In this chapter these differences are illustrated for a specific class of differential operators on [0, ∞). The operators involved do not have a compact resolvent. Their spectra and essential spectra are described. Also, the Green’s function and the Fredholm characteristics are computed explicitly. The first four sections concern first order constant coefficient differential operators. Applications to Wiener-Hopf integral equations appear in the fifth section. In the last section the results are extended to higher order differential operators on [0, ∞).