Rank one perturbations of not semibounded operators

DOI10.1007/BF01192120zbMath0901.47004OpenAlexW2094078819MaRDI QIDQ1378121

Sergio A. Albeverio, Pavel Kurasov

Publication date: 4 March 1998

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01192120

zbMATH Keywords

one parameter semigroupKrein's formulaDirac operators with point interactionextension theory for symmetric operatorsform unbounded rank one perturbationsnecessarily semiboundedrank one perturbations of selfadjoint operatorsrenormalization of the coupling constant

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Perturbation theory of linear operators (47A55) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Applications of operator theory to differential and integral equations (47N20) Dilations, extensions, compressions of linear operators (47A20)

Related Items (16)

Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators ⋮ On approximations of rank one ℋ₋₂-perturbations ⋮ Rank one perturbations and singular integral operators ⋮ Rank one perturbations, approximations, and selfadjoint extensions ⋮ On rank one perturbations of selfadjoint operators ⋮ Rank one perturbations of not semibounded operators ⋮ Random Sturm–Liouville operators with point interactions ⋮ Computation of the unitary group for the Rashba spin–orbit coupled operator, with application to point-interactions ⋮ Finite rank singular perturbations and distributions with discontinuous test functions ⋮ Time ordering and counting statistics ⋮ Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations ⋮ Triplet extensions. I: Semibounded operators in the scale of Hilbert spaces ⋮ Characteristic operator functions for quantum input-plant-output models and coherent control ⋮ INVERSE SPECTRAL PROBLEMS FOR SINGULAR RANK-ONE PERTURBATIONS OF A HILL OPERATOR ⋮ Nevanlinna Functions, Perturbation Formulas, and Triplets of Hilbert Spaces ⋮ Finite-rank perturbations of the Dirac operator

Cites Work

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• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• Rank one perturbations, approximations, and selfadjoint extensions
• On rank one perturbations of selfadjoint operators
• Rank one perturbations of not semibounded operators
• Rank one perturbations at infinite coupling
• Rank one perturbations with infinitesimal coupling
• Distribution theory for discontinuous test functions and differential operators with generalized coefficients
• Finite rank singular perturbations and distributions with discontinuous test functions
• Square Powers of Singularly Perturbed Operators

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