Spectral analysis of nonselfadjoint Schrödinger operators with a matrix potential

Dissipative Schrödinger operators with a matrix potential are studied in L2((0,∞);E)(dimE=n<∞) which are extension of a minimal symmetric operator L0 with defect index (n,n). A selfadjoint 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 Schrödinger operator are proved.