Extensions, dilations and functional models of infinite Jacobi matrix
CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.55, sa.3, ss.593-609, 2005 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 55 Sayı: 3
- Basım Tarihi: 2005
- Doi Numarası: 10.1007/s10587-005-0048-3
- Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.593-609
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on the completeness of the system of eigenvectors and associated vectors of dissipative operators.