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Scattering theory, a powerful method for the analysis of PDEs, represents one of the most important developments in mathematical physics of recent decades. This classic book is ideal 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. The exposition is based on a rigorous treatment of the Riesz-Fredholm theory of compact operators in dual systems, followed by a derivation of the jump conditions and mapping properties of scalar and vector potentials in spaces of continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. The reader will find 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 a function-theoretic approach.
David Colton is Unidel Professor of Mathematics at the University of Delaware. He is the author or coauthor of six books, including The Linear Sampling Method in Inverse Electromagnetic Scattering (2011), written with Fioralba Cakoni and Peter Monk. Rainer Kress is a Full Professor of Numerical and Applied Mathematics at the University of Gottingen. He has been a member of the Gottingen Academy of Sciences since 1995 and Professor Emeritus since 2010. He is the author or coauthor of five books.
Preface to the Classics Edition; Preface; Symbols; 1. The Riesz-Fredholm theory for compact operators; 2. Regularity properties of surface potentials; 3. Boundary-value problems for the scalar Helmholtz equation; 4. Boundary-value problems for the time-harmonic Maxwell equations and the vector Helmholtz equation; 5. Low frequency behavior of solutions to boundary-value problems in scattering theory; 6. The inverse scattering problem: exact data; 7. Improperly posed problems and compact families; 8. The determination of the shape of an obstacle from inexact far-field data; 9. Optimal control problems in radiation and scattering theory; References; Index.
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- ID: 9781611973150
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