Spectral Analysis, Model Theory and Applications of Finite-Rank Perturbations

DOI10.1007/978-3-030-43380-2_9arXiv1904.09833MaRDI QIDQ6317557

Publication date: 11 April 2019

Abstract: This survey focuses on two main types of finite-rank perturbations: self-adjoint and unitary. We describe both classical and more recent spectral results. We pay special attention to singular self-adjoint perturbations and model representations of unitary perturbations.

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Research exposition (monographs, survey articles) pertaining to operator theory (47-02)

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