Dissipative second-order difference operators with general boundary conditions
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, cilt.10, sa.1, ss.1-16, 2004 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 1
- Basım Tarihi: 2004
- Doi Numarası: 10.1080/1023619031000110912
- Dergi Adı: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1-16
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
A space of boundary values is constructed for minimal symmetric second-order difference operator in the Hilbert space I w 2 (Z) (Z:{0,+/-1,+/-2,...}) with defect index (2,2) (in Weyl's limit-circle cases at +/-infinity). A description of all maximal dissipative (accretive), selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions at +/-infinity. We investigate maximal dissipative operators with, generally speaking, nonseparated boundary conditions. In particular, if we consider separated boundary conditions, that at -infinity and infinity nonselfadjoint (dissipative) boundary conditions are prescribed simultaneously. 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 also construct a functional model of maximal dissipative operator and determine its characteristic function. We prove a theorem on completeness of the system of eigenvectors and associated vectors of the maximal dissipative operator.