Rank one perturbations at infinite coupling in Pontryagin spaces.

DOI10.1016/j.jfa.2003.06.005zbMath1068.47041OpenAlexW2005829122WikidataQ124629955 ScholiaQ124629955MaRDI QIDQ1431785

Yuri Shondin, Aalt Dijksma, Heinz K. Langer

Publication date: 11 June 2004

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

Full work available at URL: https://pure.rug.nl/ws/files/2946842/2004JFunctAnalDijksma.pdf

zbMATH Keywords

Hilbert spaceoperatorsymmetricrank one perturbation\(Q\)-functionPontryagin spacegeneralized Nevanlinna functionextension theorydefect functioninfinite couplingself-adjoint linear relation

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Linear relations (multivalued linear operators) (47A06) Linear operators on spaces with an indefinite metric (47B50) Ordinary differential operators (34L99)

Related Items (7)

Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces ⋮ Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints ⋮ Bessel-type operators with an inner singularity ⋮ An operator theoretic interpretation of the generalized Titchmarsh-Weyl coefficient for a singular Sturm-Liouville problem ⋮ Approximation of N κ ∞ -functions I: Models and Regularization ⋮ On some extensions of the A-model ⋮ Distributional representations of Nκ(∞)‐functions

Cites Work

• Unitary colligations in \(\pi _ k\)-spaces, characteristic functions and Shtraus extensions
• Extensions of Laguerre operators in indefinite inner product spaces
• Singular point-like perturbations of the Bessel operator in a Pontryagin space
• Rank one perturbations in a Pontryagin space with one negative square
• Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
• Rank one perturbations at infinite coupling
• Rank one perturbations with infinitesimal coupling
• A factorization result for generalized Nevanlinna functions of the class \(N_k\)
• Scattering from generalized point interactions using self-adjoint extensions in Pontryagin spaces
• Sturm-Liouville operators with an indefinite weight function
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