Nevanlinna Functions, Perturbation Formulas, and Triplets of Hilbert Spaces

DOI10.1002/mana.19981950107zbMath0921.47019OpenAlexW2143286270MaRDI QIDQ4224704

Hassi, Seppo, Hendrik S. V. de Snoo

Publication date: 30 September 1999

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19981950107

zbMATH Keywords

Nevanlinna functions\(Q\)-functionselfadjoint extensionsgeneralized Friedrichs extensionclosed symmetric operatorgraph perturbationsgraph restriction

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) Linear operator methods in interpolation, moment and extension problems (47A57) Dilations, extensions, compressions of linear operators (47A20) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (7)

On rank one perturbations of selfadjoint operators ⋮ On Matrix-Valued Herglotz Functions ⋮ On matrix‐valued Herglotz‐Nevanlinna functions with an emphasis on particular subclasses ⋮ One-dimensional Perturbations, Asymptotic Expansions, and Spectral Gaps ⋮ Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations ⋮ Generalized resolvent matrices and spaces of analytic functions ⋮ Interpolation theory in sectorial Stieltjes classes and explicit system solutions

Cites Work

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• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• Rank one perturbations of not semibounded operators
• Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
• Rank one perturbations at infinite coupling
• The inverse spectral problem for canonical systems
• On some subclasses of Nevanlinna functions
• Distribution theory for discontinuous test functions and differential operators with generalized coefficients
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• Hermitian bilinear forms which are not semibounded

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