Dissipative eigenvalue problems for a singular Dirac system


Allahverdiev B.

APPLIED MATHEMATICS AND COMPUTATION, vol.152, no.1, pp.127-139, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 152 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.1016/s0096-3003(03)00550-2
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.127-139

Abstract

Dissipative singular Dirac operators are studied in the space L-A(2) ([a,b) ; C-2) (-infinity < a < b less than or equal to infinity), that the extensions of a minimal symmetric operator in Weyl's limit-point case. We construct a selfadjoint dilation 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 specify its characteristic function in terms of the Titchmarsh-Weyl function of selfadjoint operator. We prove theorems on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operators. (C) 2003 Elsevier Inc. All rights reserved.