The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

By computerized tomography (CT) we mean the reconstruction of a function from its line or
plane integrals, irrespective of the field where this technique is applied. In the early 1970s …

2 Introduction that the law of formation has been found. The corresponding direct problem is
to evaluate the sequence (an) given the law of formation. It is clear that such inverse …

The lectures presented in this book were given at the University of Bonn in the academic
year 1983/4 and in part at the University of Strathclyde, Glasgow. Their aim was to introduce …

In a celebrated paper “Can one hear the shape of a drum?” M. Kac [Am. Math. Monthly 73, 1
(1966)] 10.2307/2313748 asked his famous question about the existence of nonisometric …

This book for the first time unifies the theories of acoustic, electromagnetic, and elastic
waves and discusses the many physical and geometric aspects of their interactions with …

In this section we introduce some notations, formulate some properties of the potentials of
the single and double layers, and discuss the integral equations for solving the exterior …

Uniqueness theorems are obtained for the problem of determining the shape of a sound-soft
or sound-hard obstacle from a knowledge of (1) the far-field pattern at a fixed value of the …

The inverse scattering problem we are considering in this paper is to determine the shape of
an obstacle from a knowledge of the time-harmonic incident field and the phase and …

We consider a two-dimensional inverse scattering problem of determining a sound-soft
obstacle from the far field pattern and, under a non-trapping condition, we establish …