Theoretical Considerations for Inverse Scattering

摘要

Inversion Theory is a guide for handling inverse problems rather than a set of inversion techniques. The usual ill-posedness of inverse problems has first to be dealt with by reassessing the concept of solution and by giving a detailed answer to the basic mathematical questions of solutions existence, uniqueness, construction, stability, approximation. But this is not sufficient. If the results are to be used by physicists, they should take into account the fact that no physical problem can be given a complete study separately from all others. In other words, investigating mathematical questions, and in particular describing the sets of solutions, must be done in such a way that physical motivations and physical considerations are always apparent. These remarks are illustrated on several examples taken in Scattering Theory. (ERA citation 07:062303)