On form-sum approximations of singularly perturbed positive self-adjoint operators

DOI10.1006/jfan.1999.3506zbMath0944.47008OpenAlexW1978960915MaRDI QIDQ1963854

Volodymyr Koshmanenko, Sergio A. Albeverio

Publication date: 20 September 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3506

zbMATH Keywords

Sobolev spacepoint interactionapproximation by positive operatorsfinite rankgraph normstrongly singularpositive selfadjoint operatorform-sum approximationperturbations of the Laplace operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25)

Related Items (8)

Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces ⋮ ON THE PROBLEM OF THE RIGHT HAMILTONIAN UNDER SINGULAR FORM-SUM PERTURBATIONS ⋮ On approximations of rank one ℋ₋₂-perturbations ⋮ The Landau Hamiltonian with δ-potentials supported on curves ⋮ Singular perturbations with an infinite constant coupling ⋮ Singularly perturbed Hamiltonians of a quantum Rayleigh gas defined as quadratic forms ⋮ Eigenvalue asymptotics for Sturm--Liouville operators with singular potentials ⋮ On Schrödinger operators perturbed by fractal potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some remarks on the \(\delta\) '-interaction in one dimension
• On a singular part of an unbounded operator
• Quadratic forms for singular perturbations of the Laplacian
• Toward the rank-one singular perturbation theory of self-adjoint operators
• Self-adjoint operators
• A canonical decomposition for quadratic forms with applications to monotone convergence theorems
• Schrödinger operators with singular interactions
• Rank one perturbations, approximations, and selfadjoint extensions
• Symmetric form of the Hudson-Parthasarathy stochastic equation
• Generalized sum of operators
• A new class of point interactions in one dimension
• Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
• Spectral synthesis in Sobolev spaces and uniqueness of solutions of the Dirichlet problem
• Rank one perturbations at infinite coupling
• Rank one perturbations with infinitesimal coupling
• Singular perturbations with an infinite constant coupling
• On point interaction in quantum mechanics
• Krein’s formula approach to the multisolenoid Aharonov–Bohm effect
• On characteristic properties of singular operators
• Regularized approximations of singular perturbations from the h -2-class
• TOWARDS THE RIGHT HAMILTONIAN FOR SINGULAR PERTURBATIONS VIA REGULARIZATION AND EXTENSION THEORY
• Square Powers of Singularly Perturbed Operators
• Perturbations of self-adjoint operators by singular bilinear forms
• Perturbations of the Schrödinger equation by potentials with small support

This page was built for publication: On form-sum approximations of singularly perturbed positive self-adjoint operators