Asymptotics of the Jost-function for the two-dimensional Schrödinger operator

The article concerns asymptotics of the Jost function $\chi(z,\lambda)$ for the two-dimensional Schrödinger operator for the arbitrary $\lambda\in\mathbb{C}$ and $z/|z|\in S^1$ when $|z|\to\infty$ and a relation with the inverse scattering problem.