Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware. Before his death in 1998, he made major scientific contributions in the areas of electromagnetic scattering, wave propagation, and inverse problems. He was instrumental in bringing together the mathematical and engineering communities working in these fields, and actively collaborated with a number of colleagues from both communities.
It was in Professor Kleinman's memory that leading researchers in the fields of wave propagation, scattering,...

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject.
Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie...

Inverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems.
Inverse Problems and Related Topics compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting...

This Research Note in Mathematics introduces a new Morse (index) theory that is easier to use, less technical and more flexible than existing theories for strongly indefinite functionals. It also contains an extensive survey of material that is now classical but has never appeared in book form. This text provides an accessible, self-contained treatment of the subject matter with full proofs of the major results, and complete with applications of the theory to Hamiltonian systems and other areas of current research, including wave equations, Chern-Simon functionals and Lorentzian geometry.

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals.
The first part of the book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the theory...

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories.
The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory....

This Research Note introduces a new Morse (index) theory that is easie r to use, less technical, and more flexible than existing theories. Un til now, these results have appeared only in scattered journals. The a uthor provides a self-contained treatment with full proofs of the majo r results and complete with applications of the theory to Hamiltonian systems and other areas of current research, including wave equations, Chern-Simon functionals, and Lorentzian geometry

Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration.
Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory....

This volume addresses the structural aspects of complex Lie groups. It begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups - used as a primary tool in subsequent chapters - and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results...