Spectral analysis of non-selfadjoint discrete Schrodinger operators with spectral singularities

Let L denote the non-selfadjoint discrete Schrodinger operator generated in l(2)(IN) by the difference expression (ly)(n) = y(n-1) + y(n+1) + b(n)y(n), n is an element of IN = {1,2,...,} and the boundary condition y(0) = 0, where {b(n)}(n=1)(infinity) is a compl ex sequence. In this paper we investigate Weyl-Titchmarsh (W-T) function of the operator L and obtained the relation between W-T function and the gene ralized spectral function of L in the sense of MARCHENKO. Moreover we find Cauchy type integral representation of W-T function. Using this representat ion we derived the spectral expansion of L in terms of the principal vector s, taking into account the spectral singularities.