On the basisness in $L_2$(0, 1) of the root functions in not strongly regular boundary value problems

Abstract

In the present article we consider the non-self adjoint Sturm-Liouville operators with periodic and anti-periodic boundary conditions which are not strongly regular. We obtain the asymptotic formulas for eigenvalues and eigenfunctions of these boundary value problems, when the potential q(x) is a complexvalued function. Then using these asymptotic formulas, the Riesz basisness in $L_2$(0, 1) of the root functions are proved.