This book provides the principal mathematical topics commonly used in developing scattering theories and also provides an introduction to linear and non-linear scattering theories. It indicates how these various aspects might be applied to problems in mathematical physics and the applied sciences.
This book provides the principal mathematical topics commonly used in developing scattering theories and also provides an introduction to linear and non-linear scattering theories. It indicates how these various aspects might be applied to problems in mathematical physics and the applied sciences.
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.
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.
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