Dissipative Schrodinger operators with matrix potentials


Allahverdiev B.

POTENTIAL ANALYSIS, vol.20, no.4, pp.303-315, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2004
  • Doi Number: 10.1023/b:pota.0000009815.97987.26
  • Journal Name: POTENTIAL ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.303-315
  • Süleyman Demirel University Affiliated: Yes

Abstract

Maximal dissipative Schrodinger operators are studied in L-2((-infinity,infinity); E) (dim E = n < &INFIN;) that the extensions of a minimal symmetric operator with defect index (n, n) (in limit-circle case at -&INFIN; and limit point- case at &INFIN;). We construct a selfadjoint dilation of a dissipative operator, carry out spectral analysis of a dilation, use the Lax - Phillips scattering theory, and find the scattering matrix of a dilation. We construct a functional model of the dissipative operator, determine its characteristic function in terms of the Titchmarsh-Weyl function of selfadjoint operator and investigate its analytic properties. Finally, we prove a theorem on completeness of the eigenvectors and associated vectors of a dissipative Schrodinger operators.