G F Roach
An Introduction to Linear and Nonlinear Scattering Theory
G F Roach
An Introduction to Linear and Nonlinear Scattering Theory
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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.
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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.
Produktdetails
- Produktdetails
- Verlag: CRC Press
- Seitenzahl: 264
- Erscheinungstermin: 15. Mai 1997
- Englisch
- Abmessung: 241mm x 163mm x 19mm
- Gewicht: 526g
- ISBN-13: 9780582092303
- ISBN-10: 0582092302
- Artikelnr.: 23437949
- Verlag: CRC Press
- Seitenzahl: 264
- Erscheinungstermin: 15. Mai 1997
- Englisch
- Abmessung: 241mm x 163mm x 19mm
- Gewicht: 526g
- ISBN-13: 9780582092303
- ISBN-10: 0582092302
- Artikelnr.: 23437949
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.
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.
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.