Completeness theorem for the system of eigenfunctions of the complex Schr\"odinger operator ${\mathcal{L}}_c=-d^2\mathrm{/}d{x}^2+c{x}^{\alpha }$

The completeness of the system of eigenfunctions of the complex Schr"odinger operator ${\mathcal{L}}_c=-d^2\mathrm{/}d{x}^2+c{x}^{\alpha }$ on the semi-axis with Dirichlet boundary conditions is proved for $\alpha \in (0,2)$ and $|\arg c|<2\pi\alpha/(\alpha+2)+\Delta t(\alpha)$withsome$\Delta t(\alpha)>0$.