Summary

Diffraction Theory: The Sommerfeld-Malyuzhinets Technique gives detailed description of the method and its related mathematical aspects. The authors have paid much attention to manifest basic ideas and connect into the whole picture various relevant mathematics. On the other hand some modern applied problems with more complicated boundary conditions are also addressed.The development of the technique is achieved by examination of problems to those the corresponding Malyuzhinets's system of functional equations cannot be solved exactly (for example, the problem of electromagnetic wave skew incidence on an impedance wedge).Due to the localization principle the results based on the Sommerfeld-Malyuzhinets method can be exploited by the Geometrical Theory of Diffraction (GTD) or its equivalent versions for construction of the far field asymptotic solutions in various situations of research and engineering practice.