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| Авторизация |
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| Kanwal R.P. — Linear Integral Equations: Theory and Techniques |
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| Предметный указатель |
 -function 4 26 30 136 147 148 153 159
-kernel 4 26 30 133 141 143 144 146 149—152 157 158 160 161 165
-space 133 134 136 137 158 159
Abel integral equation 167 200 206 211
Acoustic diffraction by annular disk 120
Acoustic diffraction by rigid body 280
Acoustic diffraction by rigid disk 129
Acoustic diffraction by soft body 279
Acoustic diffraction by soft disk 118
Acoustic diffraction by soft sphere 280
Adjoint 18 72
Airfoil equation 209
Analytic function 30
Approximation method 23
Associated Legendre function 105
Bessel equation 83
Bessel function 104 114 138 216 232 241 277 289
Bessel operator 92
Bessel’s inequality 136 140 144 195
beta function 169 170
Biharmonic equation 123
Bilinear form 142 144 148 150 165
Born approximation 131
Boundary effects 258 273
Boundary value problem 64 67 72 76 78 79ff
Branch point 288
Capacity of circular disk 244
Capacity of condenser 255
Capacity of conductor 253 254
Capacity of sphere 248 249
Cauchy principle value 170 174 175 177
Cauchy sequence 134
Cauchy type integral 176—178 180 181 184 187
Cauchy — Riemann equations 186
Cauchy’s integral formula 128
Cauchy’s integral theorem 128 179
Charge density 101 103
Compact set 159
Complete continuity 159—161
Completeness 134 150
Consistency condition 81 82 86—88 102 109
Contour integral 176 288
Convergence in mean 136 147
Convolution integral 5 197—200
Crack problem 276 278
Degenerate kernel 4 8
Difference kernel 5 199
Dilation vector 130 272—274
Dimensionless parameter see "Perturbation parameter"
Dirac delta function 70
Dirac delta function, sifting property of 70 96 217
Dirichlet condition 94
Dirichlet problem 98—100 107 117 129
Displacement vector 130
Distributions 71
Divergence theorem 95
Eigenfunction 6ff
Eigenvalue 6ff
Eigenvalue, index of 17
Eigenvalue, multiplicity of 17 55 57 141
Elastic bar 68
Elastic bar, bending rigidity of 69
Elastic bar, transverse oscillations of 68
Elastic half-space 120 284
Elastic half-space, torsion 216 222
Elastic half-space, torsional oscillations 120 231 237
Elastic medium, cavity in 275
Elastic medium, crack in 276
Elastic medium, inclusions in 275 284
Elastic medium, Lame’s constants of 130
Elasticity 272 275 276
Elastodynamics 273 274
Elastostatics 272
Electrostatic potential 96 254 283
Electrostatic potential of annular disk 113
Electrostatic potential of axially symmetric conductor 113
Electrostatic potential of circular disk 103 110 243
Electrostatic potential of spherical cap 245 246
Electrostatics 253 263
Entire function 35 40
Exciting force 274
Extremal principle 161
Faltung 6
Far-field amplitude 281 282
Fourier expansion 114 135 136 146—148 157 262 263 277
Fourier integral 194
Fourier series see "Fourier expansion"
Fourier transform 66 114 195 196 198
Fredholm alternative 14 20
Fredholm integral equation 2
Fredholm theory 41
Fredholm’s determinant 45 46
Fredholm’s minor 52 53 60
Fredholm’s series 45 47—49 55 58
Fredholm’s theorem 16 43 48 51 57 59
Functional analysis 158
Fundamental solution 96 116
Geometric series 28 32 38 111
Gram — Schmidt procedure 135 140 141 165
Green’s formula 72
Green’s function 72 77 80 116 121ff
Green’s function, causal 75
Green’s function, free space 96 107 116 118
Green’s function, modified 86 87
Green’s identities 95
Green’s tensor 123 124 126 130 258 268 272—274
Green’s vector 123 124 126 258 268
Hankel function 232 241
Harmonic function 95 97 102 186 262
Heat conduction 126
Heaviside function 71 78
Helmholtz equation 94 96 116 118 121
Hermitian matrix 142
Hilbert formula 187—189
Hilbert kernel 184 185 190
Hilbert space 133 137
Hilbert transform, finite 207—209 212
Hilbert transform, infinite 210 213
Hilbert type integral equation 187 188 190 209
Hilbert — Schmidt theorem 146 148 150 151 165
Hoelder condition 175 177
Hoelder continuous 175—178 180
Hypergeometric function 226 227
Index of eigenvalue 17
Influence function 75
Initial value problem 61 67 72—74ff
Inner product 6 134
Integrable function 3
Integral equation 3
Integral equation of first kind 2
Integral equation of second kind 3
Integral equation of third kind 3
Integral equation, Fredholm 2
Integral equation, homogeneous 3
| Integral equation, linear 2
Integral equation, singular 3 167ff
Integral equation, Volterra 3
Integral representation formula 61 75 96 107 255 260—262 265
Integral transform methods 195
Integrodifferential equation 38
Iterated kernels 27 29 31 35 199
Iterative scheme 26
Kernel 3
Kernel, complex-symmetric 132
Kernel, degenerate 4 8ff
kernel, hermitian 13 132
Kernel, negative definite 149 150
Kernel, nonnegative definite 149 150
Kernel, nonpositive definite 149 150
Kernel, positive definite 149 150 164
Kernel, separable 4 8ff
kernel, symmetric 5 133
Kernel, truncated 143 145 148
Kinematic viscosity 124
Kronecker delta 104
Lagrange multipliers 162
Laplace equation 94 95 101 107ff
Laplace transform 70 197—199 201—203 205
Laplacian 95
Lebesgue integral 4
Legendre function 105
Legendre operator 90
Legendre polynomial 138 164 247 256 281 283
Linear independence 5
Linear operator 2 196
Lipschitz condition 175
Low — Reynolds number hydrodynamics 257
Maximum-minimum principle 161
Mehler — Dirichlet integral 247
Mercer’s theorem 149 150
Method of images 107 110 121
Method of successive approximations 26
Metric 133
Metric, natural 133 134
Metric, space 134
Minkowski inequality 8 133
Mixed boundary value problem 94 214
Modified Bessel function 114 138 277
Navier — Cauchy equations 272
Neumann condition 94
Neumann problem 99 101—103 109 117 280
Neumann series 27 29—31ff
Norm 6 133
Operator, adjoint 72 180
Operator, Bessel 92
Operator, bounded 158—160
Operator, completely continuous 159—161
Operator, Fredholm 134
Operator, Legendre 90
Operator, linear 2 196
Operator, method 158
Operator, self-adjoint 72 89 90 93 147
Ordinary differential equation 61
Orthogonal functions 6 135
Orthonormal functions 135—138ff
Oseen flow, rotary motion in 269 271
Oseen flow, steady 124
Oseen flow, steady-state vibrations in 283
Oseen flow, translational motion in 268
Parseval’s identity 137 157
Partial differential equation 94
Partial differential equation, elliptic 94
Partial differential equation, hyperbolic 94
Partial differential equation, parabolic 94
Perturbation methods 250
Perturbation parameter 120 227 239 240 250 257 263
Picard’s method 26
Plemelj formulas 178 180 182 185
Poincare — Bertrand formula 179 181 182
Poisson’s equation 94 96 101
Poisson’s integral formula 107 128
Pole 176 211
Potential layer 97 117
Potential layer, double 97 98 100 103 129 280
Potential layer, single 97 101 102 117 127 129 279
Potential layer, volume 97 117 127
Pressure 123
Principal axes of resistance 259
Radiation condition 118 129 274 279 281
Rayleigh — Ritz method 161 162 163 164
Regular curve 176
Regularity conditions 3
Representation formula see "Integral representation formula"
Residue 211
Resistance tensor 258—260
Resolvent kernel 11-13ff
Reynolds number 124 125 257 269
Riemann Hilbert problem 182 183
Riemann integral 4 173 175
Riesz — Fischer theorem 136 149 152
Scalar product 6
Scattering cross section 282
Schroedinger equation 131
Schwarz inequality 6 28 29 38 133ff
Separable kernel 4 8
shear modulus 120
Shear viscosity 261
Sine transform 195
Singular integral equation 3 167
Singular integral equation, weakly 170
Sonine integral 217
Source density 263 266 271
Spherical harmonics 105
Square integrable function 3
Stokes flow, boundary effects in 258
Stokes flow, longitudinal oscillations in 260
Stokes flow, rotary motion in 261 269 275
Stokes flow, rotary oscillations in 264 271
Stokes flow, steady 123 257
Sturm — Liouville problem 80
Tangential stress 263
Taylor’s Theorem 259
Three-part boundary value problem 219
Three-part boundary value problem, generalized 234
torque 228 265 267 268 271 283
Trace of kernel 133 149
Traction field 273
Traction tensor 273 275
TRANSPOSE 18—20 57—60
Trial function 163
Two-part boundary value problem 214
Two-part boundary value problem, generalized 229
Variational Principle 161
Velocity potential 118
Velocity vector 123
Volterra integral equation 3
Weakly singular kernel 170
wronskian 74
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