Absence of high-energy spectral concentration for Dirac systems with divergent potentials
2005 ◽
Vol 135
(4)
◽
pp. 689-702
◽
Keyword(s):
It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.
2005 ◽
Vol 135
(4)
◽
pp. 689-702
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