A forbidden set for embedded eigenvalues
Rafael René del Río Castillo
- Vol. 121, Iss: 1, pp 77-82
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In this article, the authors studied the problem of embedding eigenvalues to the spectrum of a Sturm-Liouville operator in the half axis when this spectrum is a perfect set.Abstract:
We study the problem of embedding eigenvalues to the spectrum of a Sturm-Liouville operator in the half axis when this spectrum is a perfect set. We prove the existence of an uncountable dense subset of the spectrum for which, by modifying the condition at the left or by locally perturbing the potential, it is not possible to add any eigenvalues.read more
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Spectral analysis of rank one perturbations and applications
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Operators with singular continuous spectrum. II. Rank one operators
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Singular continuous spectrum is generic
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References
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Book
Spectral Theory of Ordinary Differential Operators
TL;DR: In this paper, the separation of the Dirac operator was discussed and the Lagrange identity for n>2 was proved for the case of Dirac systems with self-adjoint differential expressions.