On the riesz basisness of root functions of a sturm–liouville operator with conjugate conditions
Yükleniyor...
Dosyalar
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maik Nauka/Interperiodica/Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Riesz basis, Periodic and antiperiodic boundary conditions, Sturm–Liouville operator
Kaynak
Lobachevskii Journal of Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
41
Sayı
9
Künye
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.
