Dissipative Schrodinger operators with matrix potentials

摘要

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.