Preface to the Classics Edition ................................ xi
Preface ........................................................ xv
Symbols ...................................................... xiii
1 The Riesz-Fredholm Theory for Compact Operators ............. 1
1.1 Compact Operators ....................................... 2
1.2 The Riesz Theory ........................................ 9
1.3 The Fredholm Theory .................................... 16
1.4 A Singular Perturbation Problem ........................ 23
1.5 Successive Approximations .............................. 26
2 Regularity Properties of Surface Potentials ................. 31
2.1 Geometry of Surfaces ................................... 32
2.2 Holder Continuity ...................................... 37
2.3 Weakly Singular Integral Operators on Surfaces ......... 39
2.4 Single- and Double-Layer Potentials .................... 46
2.5 Derivatives of Single- and Double-Layer Potentials ..... 51
2.6 Vector Potentials ...................................... 58
2.7 Integral Operators for Boundary-Value Problems ......... 61
3 Boundary-Value Problems for the Scalar Helmholtz Equation ... 65
3.1 Time-Harmonic Acoustic Scattering ...................... 66
3.2 Green's Representation Theorem and Sommerfeld's
Radiation Condition .................................... 68
3.3 The Dirichlet and Neumann Boundary-Value Problems:
Uniqueness Theorems .................................... 75
3.4 The Existence of Solutions to the Dirichlet and
Neumann Problems ....................................... 79
3.5 Boundary Integral Equations of the First Kind .......... 87
3.6 Modified Integral Equations ............................ 90
3.7 The Impedance Boundary-Value Problem ................... 97
3.8 The Transmission Boundary-Value Problem ................ 99
3.9 Integral Equations Based on the Representation
Theorems .............................................. 102
3.10 The Two-Dimensional Case .............................. 106
4 Boundary-Value Problems for the Time-Harmonic Maxwell
Equations and the Vector Helmholtz Equation ................ 108
4.1 Time-Harmonic Electromagnetic Scattering .............. 109
4.2 Representation Theorems and Radiation Conditions ...... 110
4.3 The Boundary-Value Problems for a Perfect Conductor:
Uniqueness Theorems ................................... 121
4.4 Existence of Solutions to the Electromagnetic
Boundary-Value Problems by Integral Equations of the
Second Kind ........................................... 126
4.5 Boundary Integral Equations of the First Kind ......... 136
4.6 Modified Integral Equations ........................... 140
4.7 The Impedance Boundary-Value Problem .................. 146
4.8 Integral Equations Based on the Representation
Theorems .............................................. 147
5 Low Frequency Behavior of Solutions to Boundary-Value
Problems in Scattering Theory .............................. 150
5.1 Iterative Methods for Solving the Exterior Dirichlet
and Neumann Problems .................................. 151
5.2 Iterative Methods for Electromagnetic Problems ........ 154
5.3 Low Wave Number Behavior of Solutions to the
Exterior Electromagnetic Boundary-Value Problems ...... 158
6 The Inverse Scattering Problem: Exact Data ................. 173
6.1 Entire Functions of Exponential Type .................. 175
6.2 Far-Field Patterns and Their Classification ........... 182
6.3 Uniqueness of Solutions to the Inverse
Scattering Problem .................................... 192
7 Improperly Posed Problems and Compact Families ............. 197
7.1 A Priori Assumptions and the Solution of Improperly
Posed Problems ........................................ 198
7.2 Linearized Improperly Posed Problems in Scattering
Theory ................................................ 206
7.3 Normal Families of Univalent Functions ................ 211
8 The Determination of the Shape of an Obstacle from Inexact
Far-Field Data ............................................. 219
8.1 A Model Problem ....................................... 221
8.2 The Determination of the Shape of an Obstacle in  2 ... 232
8.3 The Determination of the Shape of an Obstacle in 3 ... 239
9 Optimal Control Problems in Radiation and Scattering
Theory ..................................................... 244
9.1 Weak Compactness in Hilbert Space ..................... 245
9.2 Optimal Control for a Radiation Problem ............... 247
9.3 Optimal Control for a Scattering Problem .............. 254
References .................................................... 261
Index ......................................................... 269
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