The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\)
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Publication:1359480
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)
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]
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