On the Domain of a Magnetic Schrödinger Operator with Complex Electric Potential

Abstract

The aim of this paper is to review and compare the spectral properties of the Schrödinger operators - Δ+ U (U≥ 0) and - Δ+ iV in L2(Rd) for C∞ real potentials U or V with polynomial behavior. The case with magnetic field will be also considered. We present the existing criteria for essential self-adjointness, maximal accretivity, compactness of the resolvent, and maximal inequalities. Motivated by recent works with X. Pan, Y. Almog, and D. Grebenkov, we actually improve the known results in the case with purely imaginary potential.