Bounds on the number of bound states for potentials with critical decay at infinity

DOI10.1063/1.528750zbMath0699.46057OpenAlexW2065393458MaRDI QIDQ3477521

Joachim Stubbe

Publication date: 1990

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528750

zbMATH Keywords

Schrödinger operatorsharp Sobolev inequalities

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General theory of partial differential operators (47F05) Miscellaneous applications of functional analysis (46N99)

Related Items (3)

On Lieb-Thirring inequalities for Schrödinger operators with virtual level ⋮ Remarks on inequalities of Hardy-Sobolev type ⋮ Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups

Cites Work

• On the Schrödinger equation and the eigenvalue problem
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• New estimates on the number of bound states of Schrödinger operators
• Corrections to the classical behavior of the number of bound states of Schrödinger operators
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Bounds on the number of eigenvalues of the Schrödinger operator
• On the Number of Bound States in a Central Field of Force

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