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Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

This book is an overview of scattering theory. The author shows how this theory provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. In the first two lectures the author describes the simple and fundamental case of the Laplacian on Euclidean space to introduce the theory's basic framework. In the next three lectures, he outlines various results on Euclidean scattering, and the methods used to prove them. In the last three lectures he extends these ideas to non-Euclidean settings.

This book is an overview of scattering theory. The author shows how this theory provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. In the first two lectures the author describes the simple and fundamental case of the Laplacian on Euclidean space to introduce the theory's basic framework. In the next three lectures, he outlines various results on Euclidean scattering, and the methods used to prove them. In the last three lectures he extends these ideas to non-Euclidean settings.

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

This IMA Volume in Mathematics and its Applications MICROLOCAL ANALYSIS AND NONLINEAR WAVES is based on the proceedings of a workshop which was an integral part of the 1988- 1989 IMA program on "Nonlinear Waves." We thank Michael Beals, Richard Melrose and Jeffrey Rauch for organizing the meeting and editing this proceedings volume. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE Microlocal analysis is natural and very successful in the study of the propagation of linear...