Abstract
We discuss abstract Birman—Schwinger principles to study spectra of self-adjoint operators subject to small non-self-adjoint perturbations in a factorised form. In particular, we extend and in part improve a classical result by Kato which ensures that the spectrum does not change under small perturbations. As an application, we revisit known results for Schrödinger and Dirac operators in Euclidean spaces and establish new results for Schrödinger operators in three-dimensional hyperbolic space.
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Acknowledgements
We thank the anonymous referee for valuable comments. We are grateful to Yehuda Pinchover for useful discussions. M. H. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Project number HA 7732/2-2. The work of D. K. was partially supported by the EXPRO grant No. 20-17749X of the Czech Science Foundation (GAČR).
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Hansmann, M., Krejčiřík, D. The abstract Birman—Schwinger principle and spectral stability. JAMA 148, 361–398 (2022). https://doi.org/10.1007/s11854-022-0232-5
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DOI: https://doi.org/10.1007/s11854-022-0232-5