| Preface | p. v |
| Introduction and Outline of Contents | p. 1 |
| References and Further Reading | p. 15 |
| Some One-Dimensional Examples | p. 17 |
| Introduction | p. 17 |
| Free Problems | p. 17 |
| Solutions of the Wave Equation | p. 19 |
| Solutions of Initial Value Problems | p. 22 |
| Integral Transform Methods | p. 27 |
| On the Reduction to a First Order System | p. 31 |
| Waves on Sectionally Homogeneous Strings | p. 33 |
| A Two-Part String | p. 33 |
| A Three-Part String | p. 37 |
| Duhamel's Principle | p. 39 |
| On the Far Field Behaviour of Solutions | p. 41 |
| Jost Solutions | p. 43 |
| Some Scattering Aspects | p. 46 |
| Concluding Remarks | p. 48 |
| References and Further Reading | p. 50 |
| Preliminary Mathematical Material | p. 51 |
| Introduction | p. 51 |
| Notations | p. 51 |
| Vector Spaces | p. 52 |
| Distributions | p. 58 |
| Fourier Transforms and Distributions | p. 69 |
| References and Further Reading | p. 76 |
| Hilbert Spaces | p. 77 |
| Introduction | p. 77 |
| Orthogonality, Bases and Expansions | p. 83 |
| Linear Functionals and Operators on Hilbert Spaces | p. 91 |
| Some Frequently Occurring Operators | p. 97 |
| Unbounded Linear Operators on Hilbert Spaces | p. 105 |
| References and Further Reading | p. 114 |
| Two Important Techniques | p. 115 |
| Introduction | p. 115 |
| Spectral Decomposition Methods | p. 115 |
| Basic Concepts | p. 115 |
| Spectral Decompositions | p. 121 |
| Spectral Decompositions on Finite Dimensional Spaces | p. 122 |
| Reducing Subspaces | p. 127 |
| Spectral Decompositions on Infinite Dimensional Spaces | p. 132 |
| Functions of an Operator | p. 138 |
| Spectral Decompositions of Hilbert Spaces | p. 140 |
| Semigroup Methods | p. 145 |
| Well-posedness of Problems | p. 150 |
| Generators of Semigroups | p. 151 |
| References and Further Reading | p. 155 |
| A Scattering Theory Strategy | p. 157 |
| Introduction | p. 157 |
| Propagation Aspects | p. 158 |
| Solutions with Finite Energy and Scattering States | p. 163 |
| Construction of Solutions | p. 166 |
| Wave Operators and Their Construction | p. 169 |
| Asymptotic Conditions | p. 175 |
| A Remark about Spectral Families | p. 181 |
| Some Comparisons of the Two Approaches | p. 182 |
| Summary | p. 184 |
| References and Further Reading | p. 185 |
| An Approach to Echo Analysis | p. 187 |
| Introduction | p. 187 |
| A Typical Mathematical Model | p. 187 |
| Scattering Aspects and Echo Analysis | p. 191 |
| Construction of the Echo Field | p. 193 |
| References and Further Reading | p. 199 |
| Scattering Processes in Stratified Media | p. 201 |
| Introduction | p. 201 |
| Hilbert Space Formulation | p. 203 |
| Scattering in Plane Stratified Media | p. 209 |
| The Eigenfunctions of A | p. 213 |
| The Wave Eigenfunctions of A | p. 216 |
| Generalised Eigenfunction Expansions | p. 219 |
| Some Remarks about Asymptotic Wave Functions | p. 222 |
| References and Further Reading | p. 224 |
| Scattering in Spatially Periodic Media | p. 225 |
| Introduction | p. 225 |
| The Mathematical Model | p. 225 |
| Elements of Floquet Theory | p. 229 |
| Hill's Equation | p. 232 |
| Solutions of the Mathematical Model | p. 236 |
| References and Further Reading | p. 242 |
| Inverse Scattering Problems | p. 245 |
| Introduction | p. 245 |
| Some Asymptotic Formulae for the Plasma Wave Equation | p. 247 |
| The Scattering Matrix | p. 249 |
| Decomposable Operators | p. 250 |
| Some Algebraic Properties of W[subscript plus or minus] and S | p. 252 |
| The Inverse Scattering Problem | p. 254 |
| A High Energy Limit Method | p. 255 |
| The solution of an Integral Equation | p. 256 |
| Proof of Theorem 10.2 | p. 259 |
| References and Further Reading | p. 261 |
| Scattering in Other Wave Systems | p. 263 |
| Introduction | p. 263 |
| Scattering of Electromagnetic Waves | p. 263 |
| Overview of Acoustic Wave Scattering Analysis | p. 271 |
| More about Electromagnetic Wave Scattering | p. 274 |
| Potential Scattering in Chiral Media | p. 277 |
| Formulation of the Problem | p. 277 |
| Scattering of Elastic Waves | p. 279 |
| An Approach to Elastic Wave Scattering | p. 280 |
| References and Further Reading | p. 283 |
| Commentary | p. 285 |
| Introduction | p. 285 |
| Remarks on Previous Chapters | p. 285 |
| Appendices | p. 289 |
| Limits and Continuity | p. 289 |
| Differentiability | p. 291 |
| The Function Classes C[superscript m](B) and C[superscript m](B) | p. 291 |
| Sobolev Spaces | p. 292 |
| Retarded Potentials | p. 293 |
| An Illustration of the Use of Stone's Formula | p. 296 |
| References and Further Reading | p. 300 |
| Index | p. 307 |
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