On root functions of fractional Schrödinger operator with singular potential

Abstract

We prove a completeness in the Hilbert space $L^{2}(\mathbb{T})$ of the system of eigenfunctions and associated functions of non-selfadjoint fractional Schr\"{o}dinger operator $\mathbb{D}^{2s}u+Vu$, $s\in (1/2,1)$, on a circle with singular potential $V$ from the negative Sobolev space $H^{-s}(\mathbb{T})$.