Description
Book SynopsisFocuses on the simplest case of scattering by compactly supported potentials, and provides pointers to modern literature where more general cases are studied. The book also presents an approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Trade ReviewThis is an up to date account of modern mathematical scattering theory with an emphasis on the deep interplay between the location of the scattering poles or resonances, and the underlying dynamics and geometry. The masterful exposition reflects the authors' significant roles in shaping this very active field. A must read for researchers and students working in scattering theory or related areas." - Peter Sarnak, Institute for Advanced Study
"This is a very broad treatise of the modern theory of scattering resonances, beautifully written with a wealth of important mathematical results as well as applications, motivations and numerical and experimental illustrations. For experts, it will be a basic reference and for non-experts and graduate students an appealing and quite accessible introduction to a fascinating field with multiple connections to other branches of mathematics and to physics." - Johannes Sjostrand, Universite de Bourgogne
"Resonance is the Queen of the realm of waves. No other book addresses this realm so completely and compellingly, oscillating effortlessly between illustration, example, and rigorous mathematical discourse. Mathematicians will find a wonderful array of physical phenomena given a solid intuitive and mathematical foundation, linked to deep theorems. Physicists and engineers will be inspired to consider new realms and phenomena. Chapters travel between motivation, light mathematics, and deeper mathematics, passing the baton from one to the other and back in a way that these authors are uniquely qualified to do." - Eric J. Heller, Harvard University
Table of Contents
- Introduction
- Potential scattering: Scattering resonances in dimension one
- Scattering resonances in odd dimensions
- Geometric scattering: Black box scattering in $\mathbb{R}^n$
- Scattering on hyperbolic manifolds
- Resonances in the semiclassical limit: Resonance-free regions
- Resonances and trapping
- Appendices: Notation
- Spectral theory
- Fredholm theory
- Complex analysis
- Semiclassical analysis
- Bibliography
- Index.
