Number of Eigenvalues of Non-self-adjoint Schr\"{o}dinger Operators with   Dilation Analytic Complex Potentials
  In this paper, we give Lieb-Thirring type inequalities for isolated eigenvalues of $d$-dimensional non-selfadjoint Schr\"{o}dinger operators with complex-valued and dilation analytic potentials. In order to derive them, we prove that isolated eigenvalues and their multiplicities are invariant under complex dilation. 
Norihiro Someyama
math.SP