INVESTIGATION OF THE SPECTRUM OF THE GENERALIZED FRIDRIXS MODEL OPERATOR

This article examines the spectral properties of the generalized Fridrixs model operator, with particular emphasis on the essential spectrum, discrete eigenvalues, and the dependence of spectral characteristics on perturbation parameters. The study provides an analytical review of existing research on generalized Fridrixs models and summarizes the main approaches used to investigate the existence and number of eigenvalues. Particular attention is paid to finite-rank perturbations and their role in the formation of the discrete spectrum. The results of recent studies are analyzed to identify the main trends in the spectral theory of generalized Fridrixs models.