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Bounds for the point spectra of separated Dirac operators

Published online by Cambridge University Press:  14 November 2011

W. D. Evans  and
B. J. Harris
W. D. Evans
Affiliation:
Department of Pure Mathematics, University College, Cardiff CF1 1XL
B. J. Harris
Affiliation:
Department of Pure Mathematics, University College, Cardiff CF1 1XL
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Synopsis

In this paper real numbers A1, A2 are obtained which are such that for λ > A1 or λ < A2 there are no non-trivial solutions of the equation

which are in L2(a,∞) for some a>0. Precise values for A1 and A2 are obtained in certain cases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 1-2 , 1981 , pp. 1 - 15
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Atkinson, F. V.. Asymptotic integration and the L 2-classification of squares of second-order differential operators. Quaestiones Math. 1 (1976), 155–180.CrossRefGoogle Scholar
2Atkinson, F. V. and Everitt, W. N.. Bounds for the point spectrum for a Sturm-Liouville equation. Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 57–66.CrossRefGoogle Scholar
3Eastham, M. S. P.. On the absence of square-integrable solutions of the Sturm-Liouville equation. Lecture Notes in Mathematics 564 (Berlin: Springer, 1976).Google Scholar
4Eastham, M. S. P.. Sturm-Liouville equations and purely continuous spectra. Nieuw Arch. Wisk. 15 (1977), 169–181.Google Scholar
5Eastham, M. S. P. and McLeod, J. B.. The existence of eigenvalues embedded in the continuous spectrum of ordinary differential operators. Proc. Roy. Soc. Edinburgh Sect. A 79 (1977), 25–34.CrossRefGoogle Scholar
6Erdélyi, A.. Note on a paper by Titchmarsh. Quart. J. Math. Oxford 14 (1963), 147–152.CrossRefGoogle Scholar
7Titchmarsh, E. C.. On the nature of the spectrum in problems of relativistic quantum mechanics. Quart. J. Math. Oxford 12 (1961), 227–240.CrossRefGoogle Scholar
8Weidmann, J.. Oszillationsmethoden für Systeme gewöhnlicher Differentialgleichungen. Math. Z. 119 (1971), 349–373.CrossRefGoogle Scholar