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
Pleiades Publishing
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper we are interested in 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. Here we assume that the potentials are complex valued and continuously differentiable functions. One of conjugate conditions have different finite one-sided limits at point zero. In order to prove Riesz basisness of root functions, we firstly obtain asymptotic expressions of fundamental solutions. Putting these solutions into characteristic determinant, we get asymptotic formulas of eigenvalues by means of Rouche theorem. Asymptotic formulas of eigenfunctions acquired by obtained relation and fundamental solutions. By the aid of asymptotic formulas of eigenfunctions and Bessel properties of eigenfunctions we prove the basisness of the root functions of the boundary value problem. We also prove 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
Q2
Cilt
41
Sayı
1
Künye
Cabri, O., & Mamedov, K. R. (2020). Riesz basisness of root functions of a sturm–liouville operator with conjugate conditions. Lobachevskii Journal of Mathematics.41(1).
