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

Authors

  • Khanlar R. Mamedov Mersin University
  • Hamza Menken Mersin University

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.

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Published

2008-06-30

Issue

Vol. 1 No. 2: (April 2008)

Section

Differential Equations

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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://www.ejpam.com/index.php/ejpam/article/view/115