Spectral Properties of the Dirac Operatoron the Real Line

We study the asymptotics of the spectrum of the Dirac operator on the real line with a potential in $$L_2 $$ . It is shown that the spectrum of such an operator lies in a domain of the complex plane symmetric about the real axis and bounded by the graph of some continuous real-valued square integrable function. To prove this, we use the $$L_1 $$ -functional calculus for self-adjoint operators and a suitable similarity transformation.