The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\)

DOI10.1007/BF02559594zbMath0876.35079MaRDI QIDQ1359480

Michael Solomyak, Mikhail Sh. Birman, A. A. Laptev

Publication date: 25 November 1997

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

variational approachHardy inequalityWeyl asymptoticweak \(\ell_ q\)-space

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10)

Related Items (11)

Eigenvalues of singular measures and Connes' noncommutative integration ⋮ Weyl's laws and Connes' integration formulas for matrix-valued \(L\!\log \!L\)-Orlicz potentials ⋮ Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit ⋮ Regular and pathological eigenvalue behavior for the equation \(-\lambda u=Vu\) on the semiaxis ⋮ On the number of negative eigenvalues of an elliptic operator ⋮ Cwikel's bound reloaded ⋮ Eigenvalue asymptotics for weighted polyharmonic operator with a singular measure in the critical case ⋮ On the mathematical work of Mikhail Zakharovich Solomyak ⋮ Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case ⋮ On the mathematical work of M. Sh. Birman ⋮ Eigenvalues of the Birman-Schwinger operator for singular measures: the noncritical case

Cites Work

• Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator
• A remark on the Hardy inequalities
• One-dimensional cohomologies of discrete subgroups
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• Spectral Problems Related to the Critical Exponent in the Sobolev Embedding Theorem
• [https://portal.mardi4nfdi.de/wiki/Publication:4893803 The negative discrete spectrum of a two-dimensional Schr�dinger operator]

This page was built for publication: The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\)