The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.
Table of Contents
Second Order Elliptic Differential Operators in L2(Ω). Spectrum of the Operator L. Growth Estimates of the Generalized Eigenfunctions. Principle of Limiting Asorptions and Absolute Continuity. Examples. Spectral Representations and Scattering for Short-range perturbations. Spectral Representations and Scattering for "Long-range" perturbations. One Dimensional Schrodinger operator. Uniform Resolvent Estimates. Smoothing and Strichartz estimates. Several Topics for Evolution Equations.
Kiyoshi Mochizuki is Professor Emeritus and at Tokyo Metropolitan University, Chuo University. He is one of the authorities in spectral transforms and the scattering theory of elliptic operators of second order both on graphs and on exterior domains.