On Lieb-Thirring Inequalities for Schrödinger Operators with Virtual Level

Ekholm, Tomas; Frank, Rupert L.

doi:10.1007/s00220-006-1521-z

Cited by 54 publications

(46 citation statements)

References 13 publications

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“…In another publication [21] we prove that D 1/2 (0, V ) has a negative eigenvalue for any non-trivial V 0. This situation is associated with the existence of a virtual level at zero, as observed for example for the operator − d 2 dr 2 − 1 4r 2 in L 2 (R + ) (see [9], Proposition 3.2). In particular, the bound (6) cannot hold for ν = 1/2.…”

Section: Introductionmentioning

confidence: 85%

Lieb–Thirring and Cwickel–Lieb–Rozenblum inequalities for perturbed graphene with a Coulomb impurity

Morozov

Muller

2018

J. Spectr. Theory

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Section: Introductionmentioning

confidence: 85%

Lieb–Thirring and Cwickel–Lieb–Rozenblum inequalities for perturbed graphene with a Coulomb impurity

Morozov

Muller

2018

J. Spectr. Theory

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“…The new one-dimensional bounds involve the distance to the boundary of the interval in question and are related to Hardy-Lieb-Thirring inequalities for Schrödinger operators, see [7]. There it is shown that, for 1=2 and potentials V 2 L C1=2 .R C /, given on the half-line R C D .0; 1/, the inequality…”

Section: Introductionmentioning

confidence: 98%

Geometrical Versions of improved Berezin–Li–Yau Inequalities

Geisinger¹,

Лаптев²,

Weidl³

2011

J. Spectr. Theory

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Abstract. We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set inIn particular, we derive upper bounds on Riesz means of order 3=2, that improve the sharp Berezin inequality by a negative second term. This remainder term depends on geometric properties of the boundary of the set and reflects the correct order of growth in the semi-classical limit.Under certain geometric conditions these results imply new lower bounds on individual eigenvalues, which improve the Li-Yau inequality.Mathematics Subject Classification (2010). Primary 35P15; Secondary 47A75.

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“…In Ref. 5, it was shown that for this class of magnetic vector potentials, C ∞ c (R 3 ) is a form core for (3), allowing us to study ( − i∇ − A) 2 via (3) on smooth functions instead. Furthermore, the pointwise diamagnetic inequality holds for almost every x ∈ R 3 (see, for example, Ref.…”

Section: Introductionmentioning

confidence: 98%