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Статья

Trace formulas for Schrodinger operators with complex potentials on half-line

Letters in Mathematical Physics. 2020. Vol. 110. P. 1-20.

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.