In Ramm's second edition on refraction coefficient the author shares his recipe for creating materials with a desired refraction coefficient and solves
the many-body wave scattering problem for many small impedance bodies.
Technical problems are described which, when solved, make this theory
practically applicable. It also provides physical and mathematical arguments
for the possibility to produce such particles. Inverse scattering with
non-over-determined scattering data is discussed.
Revised and expanded,
this new edition includes three new chapters: the discussion of technological
problems to be solved for immediate applicability for creating materials with a
desired refraction coefficient; symmetry properties of the solutions to the
Helmholtz equation and new results on symmetry properties in harmonic analysis;
and theorems in inverse scattering.
- Presents a method for
creating materials with a desired refraction coefficient
- Includes a process for
creating wave-focusing materials
- Highlights inverse problems of
finding the potential from the non-over-determined scattering data
- Provides an overview of
symmetry properties in scattering theory
Alexander G Ramm, is a professor of mathematics, the author of 699 research papers and 17 research monographs, and he has edited three books. He was a Fulbright research professor in Israel and a Mercator Professor in Ukraine. He also won the Khwarizmi international award. Ramm solved inverse scattering problems with non-over-determined data, the many-body wave scattering problem when the scatterers are small particles of an arbitrary shape, and he has used this theory to give a recipe for creating materials with a desired refraction coefficient. He proved symmetry results for PDE, including a solution to the Pompeiu problem and a proof of the Schiffer's conjecture.