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, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

Audience: Integral Equation Methods in Scattering Theory can be used as a supplemental text in a graduate course on scattering theory or inverse problems and will also be of interest to research scientists in mathematics, physics, and engineering.

Contents: Preface to the Classics Edition; Preface; Symbols; Chapter 1: The Riesz-Fredholm Theory for Compact Operators; Chapter 2: Regularity Properties of Surface Potentials; Chapter 3: Boundary-Value Problems for the Scalar Helmholtz Equation; Chapter 4: Boundary-Value Problems for the Time-Harmonic Maxwell Equations and the Vector Helmholtz Equation; Chapter 5: Low Frequency Behavior of Solutions to Boundary-Value Problems in Scattering Theory; Chapter 6: The Inverse Scattering Problem: Exact Data; Chapter 7: Improperly Posed Problems and Compact Families; Chapter 8: The Determination of the Shape of an Obstacle from Inexact Far-Field Data; Chapter 9: Optimal Control Problems in Radiation and Scattering Theory; References; Index