Riesz basis property of the root functions of non-selfadjoint operators with regular boundary conditions

Abstract

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator ly ? -y? + q(x)y with periodic and antiperiodic boundary conditions that are not strongly regular, when the potential q(x) is a complex-valued absolutely continuous function and q(0) ? q(1). Using these asymptotic formulas, we prove that the root functions of these operators form a Riesz basis in the space L2(0, 1).