Spectral analysis of nonselfadjoint Schrodinger operators with a matrix potential

Dissipative Schrodinger operators with a matrix potential are studied in L-2 ((0, infinity); E) (dim E = n < infinity) which are extension of a minimal symmetric operator L-0 with defect index (n, n). A self-adjoint dilation of a dissipative operator is constructed, using the Lax-Phillips scattering theory, the spectral analysis of a dilation is carried out, and the scattering matrix of a dilation is founded. A functional model of the dissipative operator is constructed and its characteristic function's analytic properties are determined, theorems on the completeness of eigenvectors and associated vectors of a dissipative Schrodinger operator are proved. (C) 2004 Elsevier Inc. All rights reserved.