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
Resource Information
The item An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (x, 319 pages)
- 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
- Isbn
- 9781846288524
- 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
- Subject
-
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- SCIENCE -- Waves & Wave Mechanics
- 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
- 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
- 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
- 9781846288524
- 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
- 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
- 9781846288524
- 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
Subject
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Mathematics)
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Scattering (Physics) -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- Waves -- Mathematics
- SCIENCE -- Waves & Wave Mechanics
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/An-introduction-to-echo-analysis--scattering/tcH0EEteu3Y/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/An-introduction-to-echo-analysis--scattering/tcH0EEteu3Y/">An introduction to echo analysis : scattering theory and wave propagation, G.F. Roach</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
