Scattering theory in Electromagnetic Wave propagation

This talk provides an introduction and overview for electromagnetic wave propagation in the presence of perfectly conducting obstacles. Starting from the definitions, we show that exact representations, called generalized eigenfunctions, can be written terms of spherical Bessel and Hankel functions for electromagnetic waves. These generalized eigenfunctions give some idea of the topological structure of the scatterers through analysis of the scattering matrix. Through the functional calculus we can represent wave and Schroedinger propagators and provide a new technnique to analyze dispersive estimates which are important in nonlinear PDE.