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On the riesz basisness of root functions of a sturm–liouville operator with conjugate conditions

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Date

2020

Author

Cabri, Olgun
Mamedov, K. R.

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Citation

Cabri, O., & Mamedov, K. R. (2020).On te riesz basisness of root functions of a sturm–liouville operator with conjugate conditions. Lobachevskii Journal of Mathematics, 41(9), 1784-1790.

Abstract

This paper aims to prove the Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm-Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. It is assumed that the potentials of differential operator are complex valued and continuously differentiable functions and both conjugate conditions have different finite one-sided limits at point zero. In order to prove Riesz basisness of root functions, we firstly acquire asymptotic expressions of fundamental solutions. By using these solutions in the characteristic determinant, it is obtained asymptotic formulas of eigenvalues by means of Rouche theorem. Then by the aid of asymptotic formulas of eigenfunctions,Riesz basisness is shown. it is also proved the Riesz basisness of root functions of the same operator with antiperiodic boundary conditions and with same conjugate conditions.

Source

Lobachevskii Journal of Mathematics

Volume

41

Issue

9

URI

https://hdl.handle.net/11494/2495

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  • İşletme Bölümü Koleksiyonu - Makaleler [12]
  • WoS İndeksli Yayınlar Koleksiyonu [685]



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