Number of Eigenvalues of Non-Self-Adjoint Schrödinger Operators with Dilation Analytic Complex Potentials

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In the present paper, we give Lieb—Thirring type inequalities for all isolated eigenvalues of d-dimensional non-self-adjoint Schrodinger 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.