On the spectrum of second-order differential operators with complex coefficients

The main objective of this paper is to extend the pioneering work of Sims o n second-order linear differential equations with a complex coefficient, in which he obtains an analogue of the Titchmarsh-Weyl theory and classificat ion. The generalization considered exposes interesting features not visible in the special case in Sims's paper from 1957. An m-function is constructe d (which is either unique or a point on a 'limit circle'), and the relation ship between its properties and the spectrum of underlying m-accretive diff erential operators analysed. The paper is a contribution to the study of no n-self-adjoint operators; in general, the spectral theory of such operators is rather fragmentary, and further study is being driven by important phys ical applications, to hydrodynamics, electromagnetic theory and nuclear phy sics, for instance.