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E-raamat: Introduction to Linear and Nonlinear Scattering Theory [Taylor & Francis e-raamat]

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Introduction to Linear and Nonlinear Scattering TheorySuurem pilt
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781315137254
This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable, self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area. Secondly, to indicate how these various aspects might be applied to problems in mathematical physics and the applied sciences. Of particular interest will be the influence of boundary conditions.
Preface ix
Chapter 1 Introduction and outline of contents
1(10)
Chapter 2 Analytical preliminaries
11(54)
2.1 Introduction
11(1)
2.2 Preliminaries
11(9)
2.3 Distribution theory
20(15)
2.4 Hilbert space
35(6)
2.5 Bounded linear operators on Hilbert spaces
41(10)
2.6 Unbounded linear operators on Hilbert spaces
51(6)
2.7 Adjoints of unbounded operators
57(3)
2.8 A basic criterion for self-adjointness
60(5)
Chapter 3 Examples of scattering theory strategies
65(17)
3.1 Introduction
65(4)
3.2 A free problem
69(2)
3.3 Properties of the operators A0 and U0(t)
71(4)
3.4 A perturbed problem
75(2)
3.5 Comparison of solutions
77(3)
3.6 Summary
80(2)
Chapter 4 Elements of spectral theory
82(70)
4.1 Introduction
82(1)
4.2 Basic concepts
82(3)
4.3 Eigenvalues and eigenvectors
85(7)
4.4 Spectral decompositions on finite dimensional spaces
92(6)
4.5 Spectral decomposition on infinite dimensional spaces
98(3)
4.6 Properties of spectral families
101(7)
4.7 Functions of an operator
108(3)
4.8 Spectral decompositions of H
111(12)
4.9 Examples
123(17)
4.10 More on spectral decompositions associated with an operator
140(6)
4.11 On the determination of spectral families
146(6)
Chapter 5 Some applications of semigroup theory
152(17)
5.1 Introduction and basic results
152(6)
5.2 On the well-posedness of problems
158(3)
5.3 Generators of semigroups
161(6)
5.4 Perturbation of semigroups
167(2)
Chapter 6 More about wave operators
169(14)
6.1 Introduction
169(1)
6.2 Abstract evolutionary systems
169(2)
6.3 The scattering operator
171(3)
6.4 Existence of wave operators
174(2)
6.5 Selected properties of wave operators
176(5)
6.6 On the completeness of wave operators
181(2)
Chapter 7 Target scattering
183(18)
7.1 Introduction
183(1)
7.2 Concerning the incident field
183(2)
7.3 A typical target scattering problem
185(6)
7.4 Solution concepts
191(3)
7.5 Concerning existence and uniqueness of solutions
194(7)
Chapter 8 A scattering theory
201(21)
8.1 Introduction
201(1)
8.2 A free problem
202(7)
8.3 A perturbed problem
209(7)
8.4 Concerning the wave operators
216(2)
8.5 Summary and additional comments
218(4)
Chapter 9 Nonlinear scattering theory
222(18)
9.1 Introduction
222(3)
9.2 Concerning existence of solutions
225(2)
9.3 Scattering theory
227(9)
9.4 More on conditions ensuring scattering
236(4)
Chapter 10 Commentaries
240(6)
References 246(6)
Index 252
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