Dissipative Schrodinger operators with matrix potentials


Allahverdiev B.

POTENTIAL ANALYSIS, cilt.20, sa.4, ss.303-315, 2004 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 4
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:pota.0000009815.97987.26
  • Dergi Adı: POTENTIAL ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.303-315
  • Süleyman Demirel Üniversitesi Adresli: Evet

Özet

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.