Lieb-thirring Inequalities on the Half-line with Critical Exponent
نویسندگان
چکیده
We consider the operator − d 2 dr2 −V in L2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound tr „
منابع مشابه
Connection between the Lieb–Thirring conjecture for Schrödinger operators and an isoperimetric problem for ovals on the plane
To determine the sharp constants for the one dimensional Lieb– Thirring inequalities with exponent γ ∈ (1/2, 3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be attained by potentials having only one bound state. Here we exhibit a connection between the Lieb–Thirring conjecture for γ = 1 and an isporimetric inequality fo...
متن کاملA Simple Proof of Hardy-lieb-thirring Inequalities
We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).
متن کاملOn Some Sharp Spectral Inequalities for Schrödinger Operators on Semiaxis
In this paper we obtain sharp Lieb-Thirring inequalities for a Schrödinger operator on semiaxis with a matrix potential and show how they can be used to other related problems. Among them are spectral inequalities on star graphs and spectral inequalities for Schrödinger operators on half-spaces with Robin boundary conditions.
متن کاملHardy-lieb-thirring Inequalities for Fractional Schrödinger Operators
We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C|x|−2 is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and,...
متن کاملLieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
This paper is devoted to inequalities of Lieb-Thirring type. Let V be a nonnegative potential such that the corresponding Schrödinger operator has an unbounded sequence of eigenvalues (λi(V ))i∈N∗ . We prove that there exists a positive constant C(γ), such that, if γ > d/2, then
متن کامل