LAUSR

We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line. We determine trace formula: sum of imaginary part of these eigenvalues plus some singular measure plus some integral from the Jost function. Moreover, we estimate sum of imaginary part of eigenvalues and singular measure in terms of the norm of potentials. In addition, we get bounds on the total number of eigenvalues, when the potential is compactly supported.