Extensions, dilations and functional models of dirac operators

Allahverdiev B.

INTEGRAL EQUATIONS AND OPERATOR THEORY, cilt.51, sa.4, ss.459-475, 2005 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 4
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1007/s00020-003-1241-0
  • Dergi Adı: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Sayfa Sayıları: ss.459-475

Özet

A space of boundary values is constructed for minimal symmetric Dirac operator in the Hilbert space L-A(2) ((-infinity, infinity); C-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 two classes of maximal dissipative operators with separated boundary conditions, called 'dissipative at -infinity' and 'dissipative at +infinity'. In each of these cases we construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix. We construct a functional model of the maximal dissipative operator and define its characteristic function. We prove theorems on completeness of the system of eigenvectors and associated vectors of the maximal dissipative operators.