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Dergiler / European Journal of Pure and Applied Mathematics (elektronik) / 2008 / Cilt: 1 - Sayı: 2

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

Khanlar R. MAMEDOV
Hamza MENKEN
Sayfa
51–60
Yayın Tarihi
2022-10-18
DOI
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Then using these asymptotic formulas, the Riesz basisness in $L_2$(0, 1) of the root functions are proved.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:We obtain the asymptotic formulas for eigenvalues and eigenfunctions of these boundary value problems, when the potential q(x) is a complexvalued function.
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Sonuç & Katkı:Then using these asymptotic formulas, the Riesz basisness in $L_2$(0, 1) of the root functions are proved.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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 complexvalued function. Then using these asymptotic formulas, the Riesz basisness in $L_2$(0, 1) of the root functions are proved.

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Bu Makaleye Atıf Yap

MAMEDOV, K. R., MENKEN, H. (2022). On the basisness in $L_2$(0, 1) of the root functions in not strongly regular boundary value problems. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 1 - Sayı: 2, 51–60. https://ajindex.com/articles/511425

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Kaynakça (10)

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  10. V. A Marchenko, Sturm-Liouville Operators and Applications, Birkhauser Verlag, 1986.