Asymptotic behavior of generalized eigenvalues of the Schrödinger operator

The Schrödinger operator on the real line with compactly supported potential is considered. An asymptotic analysis of complex poles of the transmission coefficient $1/a(k)$ for some $\delta$-type potentials is fulfilled. We are planning to use these poles producing effective methods of approximate solutions of the inverse scattering problem in the one-dimensional case.