Extensions, dilations and functional models of discrete Dirac operators


Allahverdiev B.

ILLINOIS JOURNAL OF MATHEMATICS, vol.47, no.3, pp.831-845, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.1215/ijm/1258138196
  • Title of Journal : ILLINOIS JOURNAL OF MATHEMATICS
  • Page Numbers: pp.831-845

Abstract

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.