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Book review

Author(s) Ramm, A.G.
Title Scattering by Obstacles
Publisher D.Reidel Publishing Company
Year of publication 1986
Reviewed by Andrei Perjan

The stationary approach to the mathematical scattering theory of waves by three dimensional obstacles is expounded in this book.The author gives the quite accessible account of his investigations and of other specialists concerning the following questions: existence and uniqueness of solution to the stationary scattering problem; analytic properties of the scattering matrix; principles of limiting amplitude and limiting absorption; scattering by obstacles with infinite boundaries; scattering by small bodies; inverse scattering problems; the connection between the asymptotic behavior of solution for large time and the poles of Green function the corresponding stationary problem; numerical solution of exterior boundary value problems.

The main tools in the book are the theory of integral equations and the potential theory. There is a large bibliography and some open problems in this field of investigations are discussed here.

There is a lot of papers and even monographs dedicated to the stationary and dynamical approaches in mathematical scattering theory. The present book is good inscribed within the framework of the known bibliography.

The book contains professional level information and should be bought by the libraries. It can be useful not only for mature specialists in related arias but also for the graduate students.