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Discrete spectrum of perturbed Dirac systems with real and periodic coefficients

Published online by Cambridge University Press:  14 November 2011

Boris Buffoni
Boris Buffoni
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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Synopsis

This paper deals with the number of eigenvalues which appear in the gaps of the spectrum of a Dirac system with real and periodic coefficients when the coefficients are perturbed. The main results provide an upper bound and a condition under which exactly one eigenvalue appears in a given gap.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 337 - 347
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

1Glazman, I. M.. Direct methods of qualitative spectral analysis of singular differential operators (Jerusalem: Israel program for scientific translations, 1965).Google Scholar
2Harris, B. J.. On the spectra and stability of periodic differential equations. Proc. London. Math. Soc. (3) 41 (1980), 161–192.CrossRefGoogle Scholar
3Rofe-Beketov, F. S.. A test for the finiteness of number of discrete levels introduced into the gaps of a continuous spectrum by perturbations of a periodic potential. Soviet. Math. 5 (1964000), 689–692.Google Scholar
4Rofe-Beketov, F. S.. Deficiency indices and properties of the spectrum of some classes of differential operators. In Spectral theory and differential equations, Lecture Notes in Mathematics 448, pp. 273–293 (BerlinSpringer, 1974).Google Scholar
5Trubowitz, E.. The inverse problem for periodic potentials. Comm. Pure. Appl. Math 30 (1977) 321–337.CrossRefGoogle Scholar
6Weidmann, J.. Linear Operators in Hilbert Spaces, Graduate Texts in Mathematics 68 (Berlin:Springer, 1980).CrossRefGoogle Scholar
7Weidmann, J.. Spectral theory of ordinary differential operators, Lecture Notes in Mathematics1258 (Berlin: Springer 1987).CrossRefGoogle Scholar