Spectral Properties of Differential–Difference Symmetrized Operators

Abstract

In this paper, we propose a treatment of some class of differential–difference operators in dimension one from the spectral theory point of view. These operators emerge as symmetrizations of differential operators on (0, b), 0<b⩽∞ , admitting, in the simplest case, a decomposition of type Ld=d†d; see Sect. 2.