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

Khanlar R. Mamedov, Hamza Menken

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 complex-valued function. Then using these asymptotic formulas, the Riesz basisness in L2 (0,1) of the root functions are proved.

Keywords

Riesz basis, periodic and anti-periodic boundary conditions, regular boundary conditions, not strongly regular boundary conditions, non-self adjoint Sturm-Liouville operator, Bari's theorem.

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