Estimates for eigenvalues of Schrödinger operators with complex-valued potentials

Abstract: New estimates for eigenvalues of non-self-adjoint multi-dimensional Schr\"{o}dinger 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. Schr\"{o}dinger operators with slowly decaying potentials are also considered.