Singular point-like perturbations of the Bessel operator in a Pontryagin space

DOI10.1006/jdeq.1999.3755zbMath0960.47021OpenAlexW2160592470MaRDI QIDQ1577652

Yuri Shondin, Aalt Dijksma

Publication date: 27 August 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://pure.rug.nl/ws/files/3135618/2000JDiffEqDijksma.pdf

zbMATH Keywords

singular perturbationsBessel operatorscattering matriceseigenfunction expansionswave operatorsNevanlinna functionsnonnegative operatorgeneralized Nevanlinna classPontryagin space realization

Mathematics Subject Classification ID

Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Linear operators on spaces with an indefinite metric (47B50)

Related Items (16)

On the Weyl solution of the 1-dim Schrödinger operator with inverse fourth power potential ⋮ Generalized Nevanlinna Functions: Operator Representations, Asymptotic Behavior ⋮ Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering ⋮ Commutation methods for Schrödinger operators with strongly singular potentials ⋮ Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints ⋮ On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators ⋮ Bessel-type operators with an inner singularity ⋮ An operator theoretic interpretation of the generalized Titchmarsh-Weyl coefficient for a singular Sturm-Liouville problem ⋮ Sturm-Liouville operators with singularities and generalized Nevanlinna functions ⋮ Titchmarsh-Weyl m -functions for second-order Sturm-Liouville problems with two singular endpoints ⋮ Rank one perturbations at infinite coupling in Pontryagin spaces. ⋮ An operator theoretic interpretation of the generalized Titchmarsh-Weyl function for perturbed spherical Schrödinger operators ⋮ Characterizations of Herglotz-Nevanlinna functions using positive semi-definite functions and the Nevanlinna kernel in several variables ⋮ Approximation of N κ ∞ -functions I: Models and Regularization ⋮ On some extensions of the A-model ⋮ Distributional representations of Nκ(∞)‐functions

Cites Work

• Selfadjoint \(\Pi _{\kappa}\)-extensions of symmetric subspaces: An abstract approach to boundary problems with spectral parameter in the boundary conditions
• Extensions of Laguerre operators in indefinite inner product spaces
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• Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
• Expansion formulas for generalized hypergeometric functions
• Scattering from generalized point interactions using self-adjoint extensions in Pontryagin spaces
• Sturm-Liouville operators with an indefinite weight function
• On the Lee model
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