Rank one perturbations, approximations, and selfadjoint extensions

DOI10.1006/jfan.1996.3050zbMath0908.47010OpenAlexW1967535667MaRDI QIDQ1365230

Sergio A. Albeverio, Pavel Kurasov

Publication date: 30 November 1998

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1996.3050

zbMATH Keywords

Schrödinger operatorsdelta like potentialsselfadjoint positive operatorselfadjoint realizations of rank one perturbations

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Dilations, extensions, compressions of linear operators (47A20)

Related Items (17)

Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces ⋮ Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators ⋮ On approximations of rank one ℋ₋₂-perturbations ⋮ Rank one perturbations of not semibounded operators ⋮ Pauli-Villars regularization for some models with singular perturbations ⋮ On form-sum approximations of singularly perturbed positive self-adjoint operators ⋮ Gauge fields, point interactions and few-body problems in one dimension ⋮ An operator theoretic interpretation of the generalized Titchmarsh-Weyl function for perturbed spherical Schrödinger operators ⋮ The rigged Hilbert spaces approach in singular perturbation theory ⋮ Finite rank singular perturbations and distributions with discontinuous test functions ⋮ A Krein-like formula for singular perturbations of self-adjoint operators and applications ⋮ On symmetries in the theory of finite rank singular perturbations ⋮ Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations ⋮ Parametrization of supersingular perturbations in the method of rigged Hilbert spaces ⋮ 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

Cites Work

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• Toward the rank-one singular perturbation theory of self-adjoint operators
• 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
• Finite rank singular perturbations and distributions with discontinuous test functions
• Square Powers of Singularly Perturbed Operators

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