The perturbations of Nevanlinna type functions which preserve the set of zeros of this function or add to this set new points are discussed. 1. Statement of the problem The point spectrum in the case of rank one perturbation of purely continuous spectrum may be very rich. In general, this spectrum contains the eigenvalues as well the spectral singularities. We will not give a review of the references (we only indicate (1) and (2)). Let us consider the case where non-perturbed continuous spectrum coincides with the half line (0,1). The eigenvalues of the perturbed operator is obtained as a set of zeros of the function

F. Diaba

Papers

On rank one perturbation of continuous spectrum which generates prescribed finite point spectrum