On the basisness in L_2(0,1) of the root functions in not strongly regular boundary value problems
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.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.Downloads
Additional Files
Published
2008-06-30
Issue
Section
Differential Equations
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.
How to Cite
On the basisness in L_2(0,1) of the root functions in not strongly regular boundary value problems. (2008). European Journal of Pure and Applied Mathematics, 1(2), 51-60. https://ejpam.com/index.php/ejpam/article/view/115