On a Scientific Heritage of Victor P. Shestopalov: Critical Points of Dispersion Equations and the Theory of Intertype Interaction

A brief survey is given of the most valuable contributions of Victor P. Shestopalov to electromagnetics and diffraction theory related to the application of the spectral theory of operator-valued functions. A particular attention is paid to the creation of the theory of intertype interaction of oscillations and waves in open structures on the basis of analysis of critical points of abstract dispersion equations. Contributions to the theory made by other researchers are reported.