SELFADJOINT DILATION OF THE DISSIPATIVE SCHRÖDINGER OPERATOR AND ITS RESOLUTION IN TERMS OF EIGENFUNCTIONS

Abstract

The object of the present work is the imbedding of the spectral theory for the dissipative Schrodinger operator with absolutely continuous spectrum acting in the Hilbert space in the spectral theory of a model operator and the proof of the theorem on expansion in terms of eigenfunctions. The imbedding mentioned is achieved by constructing a selfadjoint dilation of the operator . In the so-called incoming spectral representation of this dilation the operator becomes the corresponding model operator. Next, a system of eigenfunctions of the dilation - the radiating eigenfunctions - is constructed. From these a canonical system of eigenfunctions for the absolutely continuous spectrum of the operator and its spectral projections are obtained by orthogonal projection onto .Bibliography: 22 titles.