We study the asymptotics of the spectral density of one-dimensional Dirac systems on the half-line with an angular momentum term and a potential tending to inﬁnity at inﬁnity. The problem has two singular end-points; however, as the spectrum is simple, the derivative of the spectral matrix has only one non-zero eigenvalue which we take to be the spectral density. Our main result shows that, assuming sufﬁcient regularity of the potential, there are no points of spectral concentration for large values of the spectral parameter outside a neighbourhood of a discrete set of exceptional points.
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Karl Michael Schmidt, Michael S.P. Eastham, Asymptotics of the Spectral Density for Radial Dirac Operators with Divergent Potentials. Publ. Res. Inst. Math. Sci. 44 (2008), no. 1, pp. 107–129DOI 10.2977/PRIMS/1207921078