QUADRATIC NUMERICAL RANGE AND ITS MAIN PROPERTIES

In this paper the notion of quadratic numerical range for the operator matrices of order 2 is studied and its main properties are given. Formulas for the quadratic numerical range of the generalized Friedrichs model are described. The estimates for the boundaries of the components of the quadratic numerical range allowed us to determine the location of the eigenvalues of the generalized Friedrichs model.