| Preface | p. v |
| Authors | p. ix |
| Contents | p. xi |
| Some Preliminaries from Analysis and the Theory of Wave Processes | p. 1 |
| Fourier Transform, Line Integrals of Complex-Valued Integrands, and Series in Residues | p. 1 |
| Convolution Integral Equations and the Wiener-Hopf Method | p. 6 |
| Summation of Divergent Series and Integrals | p. 9 |
| Asymptotic Estimates of Integrals | p. 12 |
| Fredholm Theory for Integral Equations of the Second Kind | p. 21 |
| Fredholm Integral Equations of the First Kind | p. 24 |
| Singular Integral Equations with a Cauchy-Type Singularity in the Kernel | p. 29 |
| Hyper-Singular Integrals and Integral Equations | p. 35 |
| Governing Equations of Hydroaeroacoustics, Electromagnetic Theory, and Dynamic Elasticity | p. 38 |
| Integral Equations of Diffraction Theory for Obstacles in Unbounded Medium | p. 45 |
| Properties of the Potentials of Single and Double Layers | p. 45 |
| Basic Integral Equations of the Diffraction Theory | p. 52 |
| Properties of Integral Operators of Diffraction Theory: General Case and Low Frequencies | p. 57 |
| Full Low-Frequency Solution for Spherical Obstacle | p. 61 |
| Application: Scattering Diagram for Obstacles of Canonical Shape | p. 65 |
| Asymptotic Character of the Kirchhoff Physical Diffraction Theory | p. 68 |
| Wave Fields in a Layer of Constant Thickness | p. 73 |
| Wave Operator in Acoustic Layer: Mode Expansion, Homogeneous and Inhomogeneous Waves | p. 73 |
| Principles of Selection of Unique Solution in Unbounded Domain | p. 76 |
| Waves in Elastic Layer | p. 82 |
| Generalized Riemann's Zeta Function and Summation of Some Oscillating Series | p. 87 |
| Application: Efficient Calculation of Wave Fields in a Layer of Constant Thickness | p. 91 |
| Waves in the Stratified Half-Plane | p. 94 |
| Analytical Methods for Simply Connected Bounded Domains | p. 101 |
| General Spectral Properties of the Interior Problem for Laplacian | p. 101 |
| Explicit Formulas for Eigenfrequencies of Round Disc | p. 107 |
| Some Variational Principles for Eigenvalues | p. 110 |
| Weyl-Carleman Theory of Asymptotic Distribution of Large Eigenvalues | p. 115 |
| Exact Explicit Results for Some Polygons | p. 119 |
| Explicit Analytical Results for Some Polyhedra | p. 125 |
| Integral Equations in Diffraction by Linear Obstacles | p. 133 |
| Integral Operators in Diffraction by Linear Screen and by a Gap in the Screen | p. 133 |
| Operator Equation in Diffraction Problem on a Crack in Unbounded Elastic Medium | p. 138 |
| High-Frequency Asymptotics in Diffraction by Linear Obstacles in Unbounded Medium | p. 142 |
| High-Frequency Asymptotics for Diffraction by Linear Obstacles in Open Waveguides | p. 145 |
| High-Frequency Diffraction by a Linear Discontinuity in the Waveguide | p. 151 |
| Waves in Elastic Half-Space. Factorization of the Rayleigh Function | p. 157 |
| Integral Equation of the Mixed Boundary Value Problem for Elastic Layer | p. 160 |
| Short-Wave Asymptotic Methods on the Basis of Multiple Integrals | p. 165 |
| Schoch's Method: Exact Representation of 3D Wave Fields by One-Dimensional Quadratures | p. 165 |
| High-Frequency Wave Fields in Elastic Half-Space | p. 169 |
| Asymptotic Nature of the Geometrical Diffraction Theory | p. 171 |
| High-Frequency Diffraction with Re-Reflections | p. 175 |
| Application: Examples of High-Frequency Multiple Diffraction | p. 180 |
| Application: Physical Diffraction Theory for Nonconvex Obstacles | p. 184 |
| Short-Wave Integral Operator in Diffraction by a Flaw in Elastic Medium | p. 186 |
| High-Frequency Asymptotics of Integral Operator in a Three-Dimensional Diffraction Theory | p. 190 |
| Inverse Problems of the Short-Wave Diffraction | p. 195 |
| Some Basic Results in a Local Differential Geometry of Smooth Convex Surfaces | p. 195 |
| Reducing Inverse Problem of the Short-Wave Diffraction to Minkowski Problem | p. 199 |
| Explicit Results for a Differential Operator of the 2D Inverse Problem | p. 201 |
| Exact Explicit Inversion of the Basic Operator in the Case of Axial Symmetry | p. 203 |
| Nonlinear Differential Operator of the Three-Dimensional Inverse Problem | p. 205 |
| Reconstruction of Nonconvex Obstacles in the High-Frequency Range: 2D Case | p. 208 |
| Reconstruction of Nonconvex Obstacles in the High-Frequency Range: 3D Case | p. 213 |
| Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary | p. 219 |
| Ill-Posed Problems for Operator Equations of the First Kind: General Properties | p. 219 |
| Regularization of Ill-Posed Problems with the Help of Smoothing Functional | p. 222 |
| Iterative Methods for Operator Equations of the First Kind | p. 226 |
| Comparison of Various Methods for Reconstruction of the Scatterer Geometry | p. 231 |
| General Inverse Diffraction Problem: Combination of Iterations and Smoothing | p. 235 |
| A Correct Treatment of Ill-Posed Boundary Equations in Acoustics of Closed Regions | p. 242 |
| Ill-Posed Method of Auxiliary Sources in Diffraction Theory | p. 248 |
| A Method of Global Random Search in Inverse Problems | p. 251 |
| Ill-Posed Problem on Reconstruction of Convex Hull of the Obstacle in Acoustic Medium | p. 253 |
| Numerical Methods for Irregular Operator Equations | p. 259 |
| Steepest Descent Method: Stability and Improvement of the Convergence | p. 259 |
| Galerkin Methods for Integral Equations of the First Kind with Weakly Singular Kernels | p. 263 |
| Integral Equations of the Physical Diffraction Theory in the Case of Nonconvex Obstacles | p. 268 |
| Numerical Methods in Singular Integral Equations with the Cauchy-Type Kernel | p. 272 |
| Numerical Methods for Hyper-Singular Integral Equations | p. 276 |
| References | p. 281 |
| Index | p. 287 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
