Spectral properties of first order ordinary differential operators with short range potentials

Abstract

The purpose of the present paper is to give a complete proof of the theorem which will be used in a paper of the second author [4].We will discuss certain spectral properties of selfadjoint ordinary differential operators of the form iA(d/dx) + V acting in L2(R)n = Σ ⊕ L2(R)n, where A is a real diagonal constant matrix and V an Hermitian matrix valued function on R which satisfies some conditions to be stated in the sequel.