Extensions, dilations and functional models of discrete Dirac operators
ILLINOIS JOURNAL OF MATHEMATICS, cilt.47, sa.3, ss.831-845, 2003 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 47 Sayı: 3
- Basım Tarihi: 2003
- Doi Numarası: 10.1215/ijm/1258138196
- Dergi Adı: ILLINOIS JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.831-845
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
A space of boundary values is constructed for minimal symmetric discrete Dirac operators in the limit-circle case. A description of all maximal dissipative, maximal accretive and self-adjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a self-adjoint dilation of a maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and its characteristic function. Finally, we prove the completeness of the system of eigenvectors and associated vectors of dissipative operators.