THE DISCRETE SPECTRUM OF SELFADJOINT OPERATORS UNDER PERTURBATIONS OF VARIABLE SIGN

DOI10.1081/PDE-100001766zbMath0983.81018MaRDI QIDQ2747889

Oleg Safronov

Publication date: 29 April 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (6)

Eigenvalues of a periodic Schrödinger operator perturbed by a fast decaying potential ⋮ Discrete spectrum of a periodic Schrödinger operator perturbed by a rapidly decaying potential ⋮ Eigenvalues of a one-dimensional Dirac operator pencil ⋮ Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices ⋮ Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices ⋮ Eigenvalue branches of the perturbed Maxwell operator M+λD in a gap of σ(M)

Cites Work

• Unnamed Item
• On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• On a theorem of Deift and Hempel
• Trapping and cascading of eigenvalues in the large coupling limit
• Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• Brownian motion, \(L^p\) properties of Schrödinger operators and the localization of binding
• Eigenvalues in gaps and decoupling by Neumann boundary conditions
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• The discrete spectrum in the gaps of the continuous one for non-signdefinite perturbations with a large coupling constant
• Discrete spectrum of the perturbed Dirac operator
• Lower bounds for the number of eigenvalue branches for the schrödinger operator H - λ W In a Gap of H: The Case of Indefinite W
• The discrete spectrum in the spectral gaps of semibounded operators with non-sign-definite perturbations

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