Spectral analysis of dissipative Schrodinger operators

Allahverdiev B., Canoglu A.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, vol.127, pp.1113-1121, 1997 (SCI-Expanded) identifier identifier


Dissipative Schrodinger operators are studied in L-2(0, infinity) which are extensions of symmetric operators with defect index (2, 2). We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix according to the scheme of Lax and Phillips. With the help of the incoming spectral representation, we construct a functional model of the dissipative operator and construct its characteristic function in terms of solutions of the corresponding differential equation. On the basis of the results obtained regarding the theory of the characteristic function, we prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operator.