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We recall a Moure theory adapted to non self-adjoint operators and we applythis theory to Schr{\"o}dinger operators with non real potentials, usingdifferent type of conjugate operators. We show that some conjugate operatorspermits to relax conditions on the derivatives of the potential that wererequired up to now.

On the Limiting Absorption Principle at zero energy for a new class of possibly non self-adjoint Schr{\"o}dinger operators