A remark on a paper by Evans and Harris on the point spectra of Dirac operators (Q2771451)

In 1981, \textit{W. D. Evans} and \textit{B. J. Harris} [Proc. R. Soc. Edinb., Sect. A 88, 1-15 (1981; Zbl 0447.34022)] derived a sufficient condition for a special case of a one-dimensional Dirac operator in the form \(-i\sigma_2 {d\over dx}+ \sigma_3+ p\sigma_1+ w+ r\), with the potential \(w\) tending to infinity, to have a purely continuous spectrum (that is with no eigenvalues). This result states that there are no \(L^2\) solutions to the corresponding eigenvalue problem. Here, \(p\) denotes the angular momentum and \(r\) the perturbation. This type of problem was first considered by \textit{E. C. Titchmarsh} [Q. J. Math., Oxf. II. Ser. 12, 227-240 (1961; Zbl 0107.07004)].NEWLINENEWLINENEWLINEIn this paper, the author presents a relatively simple proof of a criterion similar to that of Evans and Harris. The crucial observation leading to this proof was made by the author in his previous work. Under some local boundedness conditions, a function satisfying a Gronwall-type estimate is bounded. That in turn implies the boundedness of solutions to the Dirac equation with a divergent potential. The simplicity of this proof suggest additional studies of possible variations of Dirac-type spectral problems.