# Counterexample to the Laptev--Safronov conjecture

@inproceedings{Bogli2021CounterexampleTT, title={Counterexample to the Laptev--Safronov conjecture}, author={Sabine Bogli and Jean-Claude Cuenin}, year={2021} }

We prove that the Laptev–Safronov conjecture (Comm. Math. Phys. 2009) is false in the range that is not covered by Frank’s positive result (Bull. Lond. Math. Soc. 2011). The simple counterexample is adaptable to a large class of Schrödinger type operators, for which we also prove new sharp upper bounds.

## 3 Citations

Random Schr\"odinger operators with complex decaying potentials

- Mathematics, Physics
- 2022

We prove that the eigenvalues of a continuum random Schrödinger operator −∆+Vω of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an L norm of the…

Lieb-Thirring and Jensen sums for non-self-adjoint Schr\"odinger operators on the half-line

- Mathematics, Physics
- 2021

We prove upper and lower bounds for sums of eigenvalues of Lieb–Thirring type for non-self-adjoint Schrödinger operators on the half-line. The upper bounds are established for general classes of…

Improved Lieb-Thirring type inequalities for non-selfadjoint Schr\"odinger operators

- Mathematics, Physics
- 2021

p > 1, if d = 2, p ≥ d2 , if d ≥ 3. Here σd(−∆+V ) denotes the set of discrete eigenvalues, outside the essential spectrum σe(−∆ + V ) = [0,∞). The inequality (1) cannot be true for complex-valued V…

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