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

Abstract

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

v1 in Russian, v2 in English