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Absence of high-energy spectral concentration for Dirac systems with divergent potentials

Eastham, Michael S. P. and Schmidt, Karl Michael 2005. Absence of high-energy spectral concentration for Dirac systems with divergent potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135 (4) , pp. 689-702. 10.1017/S0308210500004078

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Additional Information: PDF uploaded in accordance with publisher's policy as of 28/7/14.
Publisher: Royal Society of Edinburgh
ISSN: 14737124
Date of First Compliant Deposit: 30 March 2016
Last Modified: 05 Jun 2017 01:45

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