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Creators/Authors contains: "Laptev, Ari"

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  1. ; ; ; (, Journal of Spectral Theory)
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  2. ; ; (, Transactions of the American Mathematical Society)
    We derive weighted versions of the Cwikel–Lieb–Rozenblum inequality for the Schrödinger operator in two dimensions with a nontrivial Aharonov–Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schrödinger operator acting on antisymmetric functions and obtain similar results. 
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  3. ; ; (, Annales Henri Poincaré)
    Abstract The main result of this paper is a complete proof of a new Lieb–Thirring-type inequality for Jacobi matrices originally conjectured by Hundertmark and Simon. In particular, it is proved that the estimate on the sum of eigenvalues does not depend on the off-diagonal terms as long as they are smaller than their asymptotic value. An interesting feature of the proof is that it employs a technique originally used by Hundertmark–Laptev–Weidl concerning sums of singular values for compact operators. This technique seems to be novel in the context of Jacobi matrices. 
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  4. ; ; ; ; (, Reviews in Mathematical Physics)
    null (Ed.)
    This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schrödinger operators involving Aharonov–Bohm magnetic potentials, and to some consequences. As symmetry plays an important role for establishing optimality results, we shall consider various cases corresponding to a circle, a two-dimensional sphere or a two-dimensional torus, and also the Euclidean spaces of dimensions 2 and 3. Most of the results are new and we put the emphasis on the methods, as very little is known on symmetry, rigidity and optimality in the presence of a magnetic field. The most spectacular applications are new magnetic Hardy inequalities in dimensions [Formula: see text] and [Formula: see text]. 
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