Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces

This paper represents a revised version of the lectures, delivered by author at KROMSH-2019. These lectures are devoted to describing few different ways constructing model representation for self-adjoint and unitary operators acting in Pontryagin spaces, comparison between them. Two these models based on regularized integral Krein-Langer numerical sequence generated powers (in sense spaces) operator. The steps deduce both this spectral function corresponding operator given. In (first which belongs paper), is realized as an multiplication independent variable, but space functions it acts each models. third model, introduced V. S. Shulman, his own concept quasi-vector.