On dilation, scattering and spectral theory for two-interval singular differential operators
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, cilt.58, sa.4, ss.383-392, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 58 Sayı: 4
- Basım Tarihi: 2015
- Dergi Adı: BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.383-392
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper aims to construct a space of boundary values for minimal symmetric singular impulsive-like Sturm-Liouville (SL) operator in limit-circle case at singular end points a, b and regular inner point c. For this purpose all maximal dissipative, accumulative and self-adjoint extensions of the symmetric operator are described in terms of boundary conditions. We construct a self-adjoint dilation of maximal dissipative operator, a functional model and we determine its characteristic function in terms of the scattering matrix of the dilation. The theorem verifying the completeness of the eigenfunctions and the associated functions of the dissipative SL operator is proved.