Spectral analysis of dissipative Dirac operators with general boundary conditions


Allahverdiev B.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.283, no.1, pp.287-303, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 283 Issue: 1
  • Publication Date: 2003
  • Doi Number: 10.1016/s0022-247x(03)00293-2
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.287-303

Abstract

A space of boundary values is constructed for minimal symmetric Dirac operator in 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 maximal dissipative operators with, generally speaking, nonseparated (nondecomposed) boundary conditions. In particular, if we consider separated boundary conditions, at +/-infinity the nonselfadjoint (dissipative) boundary conditions are prescribed simultaneously. We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove the theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operators. (C) 2003 Elsevier Inc. All rights reserved.