Abstract
We discuss the eigen-values problem for rank one singular perturbations \(\tilde A = A\tilde + \alpha \langle \cdot ,\omega \rangle \omega \) of a self-adjoint unbounded operator A with a gap in its spectrum. We give a constructive description of operators à which possess at least two new eigenvalues, one in the resolvent set and other in the spectrum of A.
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Albeverio, S., Dudkin, M. & Koshmanenko, V. Rank-One Singular Perturbations with a Dual Pair of Eigenvalues. Letters in Mathematical Physics 63, 219–228 (2003). https://doi.org/10.1023/A:1024421612464
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DOI: https://doi.org/10.1023/A:1024421612464