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The Resource An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach

An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach

Label
An introduction to echo analysis : scattering theory and wave propagation
Title
An introduction to echo analysis
Title remainder
scattering theory and wave propagation
Statement of responsibility
G.F. Roach
Creator
Subject
Language
eng
Summary
"This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions." "Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained introduction to an exciting research area and, for the more experienced reader, a source of information and techniques."--Jacket
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Roach, G. F.
Dewey number
531/.1133
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QC20.7.S3
LC item number
R63 2007eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Springer monographs in mathematics
http://library.link/vocab/subjectName
  • Scattering (Physics)
  • Waves
  • Scattering (Mathematics)
  • SCIENCE
  • Waves
  • Scattering (Mathematics)
  • Scattering (Physics)
  • Scattering (Mathematics)
  • Scattering (Physics)
  • Waves
Label
An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 17
  • 145
  • 5.3.1
  • Well-posedness of Problems
  • 150
  • 5.3.2
  • Generators of Semigroups
  • 151
  • 6
  • A Scattering Theory Strategy
  • 157
  • 2.3
  • 6.2
  • Propagation Aspects
  • 158
  • 6.3
  • Solutions with Finite Energy and Scattering States
  • 163
  • 6.4
  • Construction of Solutions
  • 166
  • 6.4.1
  • Solutions of the Wave Equation
  • Wave Operators and Their Construction
  • 169
  • 6.5
  • Asymptotic Conditions
  • 175
  • 6.6
  • A Remark about Spectral Families
  • 181
  • 6.7
  • Some Comparisons of the Two Approaches
  • 19
  • 182
  • 7
  • An Approach to Echo Analysis
  • 187
  • 7.2
  • A Typical Mathematical Model
  • 187
  • 7.3
  • Scattering Aspects and Echo Analysis
  • 191
  • 2.4
  • 7.4
  • Construction of the Echo Field
  • 193
  • 8
  • Scattering Processes in Stratified Media
  • 201
  • 8.2
  • Hilbert Space Formulation
  • 203
  • 8.3
  • Solutions of Initial Value Problems
  • Scattering in Plane Stratified Media
  • 209
  • 8.3.1
  • The Eigenfunctions of A
  • 213
  • 8.3.2
  • The Wave Eigenfunctions of A
  • 216
  • 8.3.3
  • Generalised Eigenfunction Expansions
  • 22
  • 219
  • 8.3.4
  • Some Remarks about Asymptotic Wave Functions
  • 222
  • 9
  • Scattering in Spatially Periodic Media
  • 225
  • 9.2
  • The Mathematical Model
  • 225
  • 2.5
  • 9.3
  • Elements of Floquet Theory
  • 229
  • 9.3.1
  • Hill's Equation
  • 232
  • 9.4
  • Solutions of the Mathematical Model
  • 236
  • 10
  • Integral Transform Methods
  • Inverse Scattering Problems
  • 245
  • 10.2
  • Some Asymptotic Formulae for the Plasma Wave Equation
  • 247
  • 10.3
  • The Scattering Matrix
  • 249
  • 10.3.1
  • Decomposable Operators
  • 27
  • 250
  • 10.3.2
  • Some Algebraic Properties of W[subscript plus or minus] and S
  • 252
  • 10.4
  • The Inverse Scattering Problem
  • 254
  • 10.5
  • A High Energy Limit Method
  • 255
  • 1
  • 2.6
  • 10.5.1
  • The solution of an Integral Equation
  • 256
  • Appendix A10.1
  • Proof of Theorem 10.2
  • 259
  • 11
  • Scattering in Other Wave Systems
  • 263
  • 11.2
  • On the Reduction to a First Order System
  • Scattering of Electromagnetic Waves
  • 263
  • 11.3
  • Overview of Acoustic Wave Scattering Analysis
  • 271
  • 11.4
  • More about Electromagnetic Wave Scattering
  • 274
  • 11.5
  • Potential Scattering in Chiral Media
  • 31
  • 277
  • 11.5.1
  • Formulation of the Problem
  • 277
  • 11.6
  • Scattering of Elastic Waves
  • 279
  • 11.6.1
  • An Approach to Elastic Wave Scattering
  • 280
  • 2.7
  • 12.2
  • Remarks on Previous Chapters
  • 285
  • A12.1
  • Limits and Continuity
  • 289
  • A12.2
  • Differentiability
  • 291
  • A12.3
  • Waves on Sectionally Homogeneous Strings
  • The Function Classes C[superscript m](B) and C[superscript m](B)
  • 291
  • A12.4
  • Sobolev Spaces
  • 292
  • A12.5
  • Retarded Potentials
  • 293
  • A12.6
  • An Illustration of the Use of Stone's Formula
  • 33
  • 296
  • 2.7.1
  • A Two-Part String
  • 33
  • 2.7.2
  • Introduction and Outline of Contents
  • A Three-Part String
  • 37
  • 2.8
  • Duhamel's Principle
  • 39
  • 2.9
  • On the Far Field Behaviour of Solutions
  • 41
  • 2.9.1
  • Jost Solutions
  • 1
  • 43
  • 2.9.2
  • Some Scattering Aspects
  • 46
  • 3
  • Preliminary Mathematical Material
  • 51
  • 3.2
  • Notations
  • 51
  • 2
  • 3.3
  • Vector Spaces
  • 52
  • 3.4
  • Distributions
  • 58
  • 3.5
  • Fourier Transforms and Distributions
  • 69
  • 4
  • Some One-Dimensional Examples
  • Hilbert Spaces
  • 77
  • 4.2
  • Orthogonality, Bases and Expansions
  • 83
  • 4.3
  • Linear Functionals and Operators on Hilbert Spaces
  • 91
  • 4.4
  • Some Frequently Occurring Operators
  • 17
  • 97
  • 4.5
  • Unbounded Linear Operators on Hilbert Spaces
  • 105
  • 5
  • Two Important Techniques
  • 115
  • 5.2
  • Spectral Decomposition Methods
  • 115
  • 2.2
  • 5.2.2
  • Spectral Decompositions
  • 121
  • 5.2.3
  • Spectral Decompositions on Finite Dimensional Spaces
  • 122
  • 5.2.4
  • Reducing Subspaces
  • 127
  • 5.2.5
  • Free Problems
  • Spectral Decompositions on Infinite Dimensional Spaces
  • 132
  • 5.2.6
  • Functions of an Operator
  • 138
  • 5.2.7
  • Spectral Decompositions of Hilbert Spaces
  • 140
  • 5.3
  • Semigroup Methods
Control code
314349843
Dimensions
unknown
Extent
1 online resource (x, 319 pages)
Form of item
online
Isbn
9781846288517
Lccn
2007922045
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-84628-852-4
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-851-7
Specific material designation
remote
System control number
(OCoLC)314349843
Label
An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 17
  • 145
  • 5.3.1
  • Well-posedness of Problems
  • 150
  • 5.3.2
  • Generators of Semigroups
  • 151
  • 6
  • A Scattering Theory Strategy
  • 157
  • 2.3
  • 6.2
  • Propagation Aspects
  • 158
  • 6.3
  • Solutions with Finite Energy and Scattering States
  • 163
  • 6.4
  • Construction of Solutions
  • 166
  • 6.4.1
  • Solutions of the Wave Equation
  • Wave Operators and Their Construction
  • 169
  • 6.5
  • Asymptotic Conditions
  • 175
  • 6.6
  • A Remark about Spectral Families
  • 181
  • 6.7
  • Some Comparisons of the Two Approaches
  • 19
  • 182
  • 7
  • An Approach to Echo Analysis
  • 187
  • 7.2
  • A Typical Mathematical Model
  • 187
  • 7.3
  • Scattering Aspects and Echo Analysis
  • 191
  • 2.4
  • 7.4
  • Construction of the Echo Field
  • 193
  • 8
  • Scattering Processes in Stratified Media
  • 201
  • 8.2
  • Hilbert Space Formulation
  • 203
  • 8.3
  • Solutions of Initial Value Problems
  • Scattering in Plane Stratified Media
  • 209
  • 8.3.1
  • The Eigenfunctions of A
  • 213
  • 8.3.2
  • The Wave Eigenfunctions of A
  • 216
  • 8.3.3
  • Generalised Eigenfunction Expansions
  • 22
  • 219
  • 8.3.4
  • Some Remarks about Asymptotic Wave Functions
  • 222
  • 9
  • Scattering in Spatially Periodic Media
  • 225
  • 9.2
  • The Mathematical Model
  • 225
  • 2.5
  • 9.3
  • Elements of Floquet Theory
  • 229
  • 9.3.1
  • Hill's Equation
  • 232
  • 9.4
  • Solutions of the Mathematical Model
  • 236
  • 10
  • Integral Transform Methods
  • Inverse Scattering Problems
  • 245
  • 10.2
  • Some Asymptotic Formulae for the Plasma Wave Equation
  • 247
  • 10.3
  • The Scattering Matrix
  • 249
  • 10.3.1
  • Decomposable Operators
  • 27
  • 250
  • 10.3.2
  • Some Algebraic Properties of W[subscript plus or minus] and S
  • 252
  • 10.4
  • The Inverse Scattering Problem
  • 254
  • 10.5
  • A High Energy Limit Method
  • 255
  • 1
  • 2.6
  • 10.5.1
  • The solution of an Integral Equation
  • 256
  • Appendix A10.1
  • Proof of Theorem 10.2
  • 259
  • 11
  • Scattering in Other Wave Systems
  • 263
  • 11.2
  • On the Reduction to a First Order System
  • Scattering of Electromagnetic Waves
  • 263
  • 11.3
  • Overview of Acoustic Wave Scattering Analysis
  • 271
  • 11.4
  • More about Electromagnetic Wave Scattering
  • 274
  • 11.5
  • Potential Scattering in Chiral Media
  • 31
  • 277
  • 11.5.1
  • Formulation of the Problem
  • 277
  • 11.6
  • Scattering of Elastic Waves
  • 279
  • 11.6.1
  • An Approach to Elastic Wave Scattering
  • 280
  • 2.7
  • 12.2
  • Remarks on Previous Chapters
  • 285
  • A12.1
  • Limits and Continuity
  • 289
  • A12.2
  • Differentiability
  • 291
  • A12.3
  • Waves on Sectionally Homogeneous Strings
  • The Function Classes C[superscript m](B) and C[superscript m](B)
  • 291
  • A12.4
  • Sobolev Spaces
  • 292
  • A12.5
  • Retarded Potentials
  • 293
  • A12.6
  • An Illustration of the Use of Stone's Formula
  • 33
  • 296
  • 2.7.1
  • A Two-Part String
  • 33
  • 2.7.2
  • Introduction and Outline of Contents
  • A Three-Part String
  • 37
  • 2.8
  • Duhamel's Principle
  • 39
  • 2.9
  • On the Far Field Behaviour of Solutions
  • 41
  • 2.9.1
  • Jost Solutions
  • 1
  • 43
  • 2.9.2
  • Some Scattering Aspects
  • 46
  • 3
  • Preliminary Mathematical Material
  • 51
  • 3.2
  • Notations
  • 51
  • 2
  • 3.3
  • Vector Spaces
  • 52
  • 3.4
  • Distributions
  • 58
  • 3.5
  • Fourier Transforms and Distributions
  • 69
  • 4
  • Some One-Dimensional Examples
  • Hilbert Spaces
  • 77
  • 4.2
  • Orthogonality, Bases and Expansions
  • 83
  • 4.3
  • Linear Functionals and Operators on Hilbert Spaces
  • 91
  • 4.4
  • Some Frequently Occurring Operators
  • 17
  • 97
  • 4.5
  • Unbounded Linear Operators on Hilbert Spaces
  • 105
  • 5
  • Two Important Techniques
  • 115
  • 5.2
  • Spectral Decomposition Methods
  • 115
  • 2.2
  • 5.2.2
  • Spectral Decompositions
  • 121
  • 5.2.3
  • Spectral Decompositions on Finite Dimensional Spaces
  • 122
  • 5.2.4
  • Reducing Subspaces
  • 127
  • 5.2.5
  • Free Problems
  • Spectral Decompositions on Infinite Dimensional Spaces
  • 132
  • 5.2.6
  • Functions of an Operator
  • 138
  • 5.2.7
  • Spectral Decompositions of Hilbert Spaces
  • 140
  • 5.3
  • Semigroup Methods
Control code
314349843
Dimensions
unknown
Extent
1 online resource (x, 319 pages)
Form of item
online
Isbn
9781846288517
Lccn
2007922045
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-84628-852-4
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
978-1-84628-851-7
Specific material designation
remote
System control number
(OCoLC)314349843

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      38.944491 -92.326012
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