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}
}
  • Martin Karuhanga
  • Published 6 March 2019
  • Mathematics
  • Journal of Mathematical Analysis and Applications

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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

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

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

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

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

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

TLDR
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

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

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

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

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

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