Fourier Integral Operators and Asymptotics for Waves

This book presents a thorough introduction to the asymptotic methods used to describe high frequency behaviors arising from the propagation of electromagnetic waves. Microlocal analysis is the rigorous mathematical focus of this book, and each chapter discusses various tools and techniques used in this branch of analysis. Topics covered include Fourier integral operators, oscillatory integrals, the method of stationary phase, and pseudo-differential calculus. A general framework of the theory of distributions and symbolic calculus is also included. Carefully crafted exercises enhance the book's utility as a teaching and self-study resource. This monograph will be useful to researchers and graduate students working in harmonic and microlocal analysis, dispersive PDEs and variable coefficients wave equations, and hyperbolic systems. With its ramifications and applications to wave propagation in optics, fluids and plasmas, Maxwell equations, Hamiltonian PDEs and transformation theory and particle physics, it will be welcomed by mathematicians, mathematical physicists, as well as engineers.