Integral Equation Methods in Scattering Theory

This classic book provides a rigorous treatment of the Riesz–Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and Hölder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from: A full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and Hölder continuous functions. An in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves. An introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.