# On the discrete spectrum of Schrödinger operators with Ahlfors regular potentials in a strip

@article{Karuhanga2019OnTD, title={On the discrete spectrum of Schr{\"o}dinger operators with Ahlfors regular potentials in a strip}, author={Martin Karuhanga}, journal={Journal of Mathematical Analysis and Applications}, year={2019} }

## 2 Citations

### Estimation of the number of negative eigenvalues of magnetic Schr\"odinger operators in a strip

- Physics
- 2021

An upper estimate for the number of negative eigenvalues below the essential spectrum for the magnetic Schrödinger operator with Aharonov-Bohm magnetic field in a strip is obtained. Its further shown…

### Eigenvalue estimates for magnetic Schrodinger operators in a waveguide

- Physics, MathematicsGulf Journal of Mathematics
- 2021

We present an upper estimate for the number of negative eigenvalues below the essential spectrum for the magnetic Schrodinger operator with Aharonov-Bohm magnetic field in a strip.

## References

SHOWING 1-10 OF 31 REFERENCES

### On negative eigenvalues of two-dimensional Schrödinger operators with singular potentials

- Mathematics
- 2019

We present upper estimates for the number of negative eigenvalues of two-dimensional Schroedinger operators with potentials generated by Ahlfors regular measures of arbitrary dimension $\alpha\in (0,…

### On negative eigenvalues of two‐dimensional Schrödinger operators

- Mathematics
- 2014

The paper presents estimates for the number of negative eigenvalues of a two‐dimensional Schrödinger operator in terms of L log L‐type Orlicz norms of the potential and proves a conjecture by N.N.…

### Estimates for the number of eigenvalues of two dimensional Schrödinger operators lying below the essential spectrum

- Mathematics
- 2016

The celebrated Cwikel-Lieb_Rozenblum inequality gives an upper estimate for the number of negative eigenvalues of Schroedinger operators in dimension three and higher. The situation is much more…

### Negative Eigenvalues of Two-Dimensional Schrödinger Operators

- Mathematics
- 2011

We prove a certain upper bound for the number of negative eigenvalues of the Schrödinger operator H = −Δ − V in $${\mathbb{R}^{2}.}$$R2.

### Bound states in waveguides with complex Robin boundary conditions

- MathematicsAsymptot. Anal.
- 2016

It is shown that discrete spectrum exists when the perturbation acts in the mean against the unperturbed boundary conditions and the first term in its asymptotic expansion in the weak coupling regime is obtained.

### Piecewise-polynomial approximation of functions fromHℓ((0, 1)d), 2ℓ=d, and applications to the spectral theory of the Schrödinger operator

- Mathematics
- 1994

For the selfadjoint Schrödinger operator −Δ−αV on ℝ2 the number of negative eigenvalues is estimated. The estimates obtained are based upon a new result on the weightedL2-approximation of functions…

### Stability of the Magnetic Schrödinger Operator in a Waveguide

- Physics, Mathematics
- 2004

Abstract The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any local enlargement of the waveguide produces eigenvalues beneath the…

### Spectral Theory and Differential Operators

- MathematicsOxford Scholarship Online
- 2018

This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and…

### On the spectrum of Robin Laplacian in a planar waveguide

- MathematicsCzechoslovak Mathematical Journal
- 2018

We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the…

### On spectral estimates for two-dimensional Schrodinger operators

- Mathematics
- 2012

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V,\ V\ge 0,$ we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues (bound states), as the…