Estimates for eigenvalues of Schrödinger operators with complex-valued potentials

Abstract

New estimates for eigenvalues of non-self-adjoint multi-dimensional Schrödinger operators are obtained in terms of $L_p$-norms of the potentials. The results extend and improve those obtained previously. In particular, diverse versions of an assertion conjectured by Laptev and Safronov are discussed. Schrödinger operators with slowly decaying potentials are also considered.

References in corpus (1)

• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials

Cited by in corpus (5)

• Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions
• Keller-type bounds for Dirac operators perturbed by rigid potentials
• Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators
• Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics
• $L_p$-spectrum and Lieb-Thirring inequalities for Schrödinger operators on the hyperbolic plane