Integral representations for spectral functions of some nonself-adjoint Jacobi matrices - Zagorodnyuk, S. M. (Methods of Functional Analysis and Topology, 2009)
We study a Jacobi matrix J with complex numbers a_n, nZ_+, in the main diagonal such that r_0 ≤ Im a_n ≤ r_1, r_0,r_1R. We obtain an integral representation for the (generalized) spectral function of the matrix J. The method of our study is similar to Marchenko’s method for nonself-adjoint differential operators.