Counterexample to the Laptev--Safronov conjecture

Abstract

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.

arXiv comment20 pages

References in corpus (6)

• Eigenvalue bounds for Schrödinger operators with complex potentials
• Carleman estimates and absence of embedded eigenvalues
• Schrödinger operator with non-zero accumulation points of complex eigenvalues
• Sharp resolvent estimates outside of the uniform boundedness range
• Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics
• Limiting absorption principle on $L^p$-spaces and scattering theory

Cited by in corpus (4)

• Schrödinger operators with complex sparse potentials
• On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials
• Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
• Effective upper bounds on the number of resonance in potential scattering