Introduction to Linear and Nonlinear Scattering Theory

Roach, G F

• Preface -- Chapter 1: Introduction and outline of contents -- Chapter 2: Analytical preliminaries -- 2.1 Introduction -- 2.2 Preliminaries -- 2.3 Distribution theory -- 2.4 Hilbert space -- 2.5 Bounded linear operators on Hilbert spaces -- 2.6 Unbounded linear operators on Hilbert spaces -- 2.7 Adjoints of unbounded operators -- 2.8 A basic criterion for self-adjointness -- Chapter 3: Examples of scattering theory strategies -- 3.1 Introduction -- 3.2 A free problem -- 3.3 Properties of the operators Ao and Uo(t) -- 3.4 A perturbed problem -- 3.5 Comparison of solutions -- 3.6 Summary -- Chapter 4: Elements of spectral theory -- 4.1 Introduction -- 4.2 Basic concepts -- 4.3 Eigenvalues and eigenvectors -- 4.4 Spectral decompositions on finite dimensional spaces -- 4.5 Spectral decomposition on infinite dimensional spaces -- 4.6 Properties of spectral families -- 4.7 Functions of an operator -- 4.8 Spectral decompositions of H -- 4.9 Examples -- 4.10 More on spectral decompositions associated with an operator -- 4.11 On the determination of spectral families -- Chapter 5: Some applications of semigroup theory -- 5.1 Introduction and basic results -- 5.2 On the well-posedness of problems -- 5.3 Generators of semigroups -- 5.4 Perturbation of semigroups -- Chapter 6: More about wave operators -- 6.1 Introduction -- 6.2 Abstract evolutionary systems -- 6.3 The scattering operator -- 6.4 Existence of wave operators -- 6.5 Selected properties of wave operators -- 6.6 On the completeness of wave operators -- Chapter 7: Target scattering -- 7.1 Introduction -- 7.2 Concerning the incident field -- 7.3 A typical target scattering problem -- 7.4 Solution concepts -- 7.5 Concerning existence and uniqueness of solutions -- Chapter 8: A scattering theory -- 8.1 Introduction -- 8.2 A free problem -- 8.3 A perturbed problem -- 8.4 Concerning the wave operators -- 8.5 Summary and additional comments -- Chapter 9: Nonlinear scattering theory -- 9.1 Introduction -- 9.2 Concerning existence of solutions -- 9.3 Scattering theory -- 9.4 More on conditions ensuring scattering -- Chapter 10: Commentaries -- References -- Index.

"Roach has taken on a difficult task and done a good job. We should all be thankful to him for having done so."-SIAM Rev. Vol 39 No 2