Extensions, dilations and functional models of discrete Dirac operators


Allahverdiev B.

ILLINOIS JOURNAL OF MATHEMATICS, cilt.47, sa.3, ss.831-845, 2003 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Konu: 3
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1215/ijm/1258138196
  • Dergi Adı: ILLINOIS JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.831-845

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.