Mochizuki K. Spectral and Scattering Theory for Second Order Partial Differential Operators

CRC Press, Taylor & Francis Group, USA, 2017. — 250 p. — (Monographs and Research Notes in Mathematics) — ISBN: 1498756026.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.Second-Order Elliptic Operators in Exterior Domain
Essential Spectrum of Self-Adjoint Operators
Statinary Equations and Functional Identities
Growth Properties of Generalized Eigenfunctions
Principle of Limiting Absorption and Absolute Continuity
Spectral Representations and Scattering for Short-Range Pertubations
Spectral Representations and Scattering 2, “Long-Range” Perturbations
One Dimensional Schr¨odinger Operators
Uniform Resolvent Estimates and Smoothing Properties
Scattering for Time Dependent Perturbations
Strichartz Estimates for Perturbed Equations
Another Approach to Growth Properties of Generalized Eigenfunctions