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We obtain the asymptotic formulas for the eigenvalues and eigenfunctions ofthe Sturm-Liouville operators with some regular boundary conditions. Usingthese formulas, we find sufficient conditions on the potential q such that theroot functions of these operators do not form a Riesz basis.

On the Basis Property of the Root Functions of Some Class of Non-self-adjoint Sturm--Liouville Operators