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| Авторизация |
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| Kanwal R.P. — Generalized functions: Theory and technique |
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| Предметный указатель |
Abel integral equation 192 414 415
Abel's formula 228
Acoustic scattering 310
Adjoint operator 38 39 211 244 245
Algebraic singularity 82—86
Algebriac operations on distributions 33
Analytic operations on distributions 36
Axially symmetric bodies 287 288
Behavior of analytic functions at the boundaries 371
Behavior of harmonic functions at the bondaries 371
Bending of a rectangular plate 332—334
Bessel equation 49 241
Bessel function 49 74
Bessel function, generalized solutions of 241
Bessel polynomial 390
Biharmonic operator 125—129 131 283
Biorthogonal set 50 376
Boundary value problem 136 208 219
Capacity 289
Capacity of a dumbbell-shaped body 291
Capacity of a prolate spheroid 294
Capacity of a slender body 294
Capacity of a sphere 296
Capacity of an elongated rod 296
Capacity of an oblate spheroid 295
Carleman-type integral equation 411
Cartesian product 169
Cauchy principal value 29 ff
Cauchy problem 283
Cauchy representation 371
Cauchy representation for a probability density 393
Cauchy representation of a distribution 371 412
Cauchy — Riemann operator 250
Causal signal 367
Causal solution 221 258
Cavities in elastic medium 293 296 297 301
Center of dilatation 322 323 326
Center of rotation 320 321 326
Central moment 396
Characteristic function 392 393
Characteristic functional 398
Characteristic lines 265
Chebyshev polynomial 379
Compact support 22 ff
Complementary error function 286
Concave function 399
Confluent hypergeometric equation 241
Convergence of distributions 59 60
Convex function 399
Convolution 169 ff
Convolution, definition 179
Convolution, Fourier transform of 194
Convolution, Laplace transform of 200
Convolution, properties 181
Correlation 398
Cost function 402 403
Cost functional 402
Couplet 318
Cumulative charge distribution 7 ff
Curvature of a curve 129 ff
Curvature, Gaussian 339
Curvature, mean 112 ff
Curvilinear coordinates 56 57 109
D'Alembert formula 193
d'Alembert's operator 246 276
Delta convergent sequence 14
Delta function 4 ff
Delta function as a Stieltjes integral 71 72
Delta function, decomposition into plane waves 100 102
Delta function, integral representation 68 149
Delta sequence 5 ff
Delta sequence with parametric dependence 60
Differential operator 21 38
Differential operator, adjoint 38 39 211 244 245
Dipole 14 ff
Dipole sequence 15 17 18 70
Dirac delta function see "Delta function"
Direct product 169 ff
Dirichlet formula 5
Dirichlet problem 311
Disk (circular), capacity of 295
Disk (circular), distribution on 335 336
Disk (circular), elastostatic displacement of 322
Disk (circular), electric polarizability tensor for 310
Disk (circular), magnetic polarizability tensor for 310
Disk (circular), polarization tensor for 305
Disk (circular), stream function for 300
Disk (circular), virtual mass tensor for 308
Distributional convergence 60 ff
Distributional derivative 36 ff
Distributional weight function 374 ff
Distributions of bounded support 185 372 373 374
Distributions of exponential growth 201
Distributions of slow growth see "Tempered"
Distributions on arbitrary lines 332
Distributions on plane curves 129 334
Distributions, algebraic operations on 33
Distributions, analytic operations on 37
Distributions, Cauchy representation of 371 372 373 411
Distributions, centrally symmetric 35
Distributions, convergence of 59 60 140
Distributions, essential point of 47
Distributions, even 35 167
Distributions, Fourier transform of 137 ff
Distributions, homogeneous 34
Distributions, integral of 214
Distributions, invariant 34
Distributions, Laplace transform of 200 ff
Distributions, odd 35 167
Distributions, order of 46
Distributions, periodic 34
Distributions, product with a function 35
Distributions, regular 26 ff
Distributions, Riesz 279 371
Distributions, singular 26 ff
Distributions, singular support of 47 48
Distributions, skew symmetric 35
Distributions, support of 47
Distributions, tempered 139 ff
Distributions, transformation properties of 52
Divergent integrals, regularization of 67 82
Double layer distribution 45 188
Double layer potential 189 254 255
Dual space 27 ff
Dumbbell-shaped bodies 290
Dumbbell-shaped bodies, capacity of 291
Dumbbell-shaped bodies, electric polarizability tensor for 310
Dumbbell-shaped bodies, magnetic polarizability tensor for 310
Dumbbell-shaped bodies, strain energy for 293
Dumbbell-shaped bodies, stream function for 293
Eigenvalue problem 227
Elastodynamics 325
Elastostatics 319
Electric polarizability tensor 308—310
Electromagnetic boundary conditions 135
Electromagnetic potentials 348
Electromagnetic wave equation 284
Elongated rod, capacity of 296 297
Elongated rod, strain energy for 297
Embedding procedure 344
Even distributions 35 167
expectation value 396
First fundamental form 112
Fourier Bessel series 74
Fourier series 65—67 73 108
Fourier transform 68 137
Fourier transform of convolutions 194 195
Fourier transform of direct product 178
Fourier transform of radial functions 160 163 164 262
Fourier transform of tempered distributions 145 ff
| Fourier transform of test functions 141—144
Fourth-order polynomial distribution 301
Fractional derivative 191
Fractional integral 191
Fredholm integral equation 288 290 303 304 312 315 319 336
Frequency response function 367
Fresnel integral 260
Functional 25 ff
Functional, linear continuous 25 ff
Functions of compact support 22 ff
Functions of slow growth 139 ff
Fundamental matrix 217 239
Fundamental solution 39 115 217
Fundamental solution of biharmonic operator 283
Fundamental solution of Cauchy — Riemann operator 250
Fundamental solution of dissipative wave equation 282
Fundamental solution of equations for elastodynamics 283 284 325
Fundamental solution of equations for elastostatics 283 319
Fundamental solution of first-order ordinary differential equation 217
Fundamental solution of fourth-order ordinary differential equation 236
Fundamental solution of heat operator 257
Fundamental solution of Helmholtz operator 261 262
Fundamental solution of Klein — Gordon operator 280
Fundamental solution of Laplace operator 132 133 252 253 254 259
Fundamental solution of nth order ordinary differential equation 238
Fundamental solution of Oseen's equations 285 286
Fundamental solution of Schroedinger operator 260
Fundamental solution of second order ordinary differential equation 218—219
Fundamental solution of second order ordinary differential equation with variable coefficients 232
Fundamental solution of Stokes equations 283
Fundamental solution of vector wave operator 284
Fundamental solution of wave operator 263 264
Gaussian coordinates 109
Gaussian distribution 392 393
Gaussian sequence 12
Generalized analytic function 371
Generalized derivative see "Distributional derivative"
Generalized electrostatic potential 288
Generalized function 2 14 27 see
Generalized function, action of 14 ff
Generalized function, even 167
Generalized function, odd 167
Generalized Gaussian process 398
Generalized solution of ordinary differential equation 212 ff
Generalized solution of partial differential equation 247 ff
Generalized stochastic process 397
Green's function 217 220
Green's matrix 239
Green's tensor 284
Hadamard finite part 77 ff
Hadamard's method of descent 248 ff
harmonic oscillator 232
Heat operator 246 257
Heaviside function 1 ff
Heaviside sequence 16 17
Heisenberg distributions 30 44 89 151
Helmholtz operator 261
Hermite polynomial 375 377 387
Hilbert problem 412
Hilbert space 397
Hilbert transform 411
Homogeneous distribution 34
Hyperbolic differential operator 283
Hyperbolic system 340 341 345
Ideal sampler 369
Impulse pair functions 28 29
Impulse response 363—367 370
Infinite singularity 347 ff
Inhomogeneous wave equation 268
Initial value problem 107 153 207 217
Input 360 ff
Integral equation, Abel's type 192 414 415
Integral equation, Carleman type 411
Integral equation, Cauchy type 410
Integral equation, Fredholm type 288 290 303 304 312 315 319 336
Integral equation, Volterra 409
Integral of a distribution 214
Integral representation of delta function 68 149
Invariant distribution 34
Inverse Fourier transform 142 ff
Investment schedule 400
Jacobi polynomial 378 379 390
Jump discontinuity 2—4 105
Kelvin dipole 320 321 326 327
Kelvin force 319
Klein — Gordon operator 276 280
Laguerre polynomial 375 377 387 388
Laplace operator 100 131 132 149 245 252 259 276
Laplace transform 199 ff
Laplace transform of convolution 200
Laplace transform of distribution 200 ff
Laplace transform of periodic function 205
Laplace transform, inverse 200 ff
Legendre polynomial 375 376 379 387
Light cone 265 ff
Linear axial distributions 298
Linear functional 25 ff
Linear operator 361 ff
Linear system 361 ff
Locally integrable function 21 ff
Logarithmic potential 253
Mach number 274—276
Magnetic polarizability tensor 308—310
Magnetohydrodynamic waves 355
Maxwell's equations 135 347 352
Moments of orthogonal polynomials 375 ff
Moving sources, line 274
Moving sources, point 273
Moving sources, surface 275
Multiindex 20 ff
Multipole 46
n-dimensional sphere, surface area 60 62
N-dimensional sphere, volume 60—62
n-dimensional wave operator 282
Neumann problem 311 315
Newtonian potential 187 253
Normal derivative operator 114 ff
Null sequence 24 ff
Oblate spheroid, capacity of 295
Oblate spheroid, electric polarizability tensor for 309
Oblate spheroid, magnetic polarizability tensor for 309
Oblate spheroid, polarization tensor for 305
Oblate spheroid, stream function for 300
Oblate spheroid, virtual mass tensor for 308
Odd distribution 35 167
Operator 360 ff
Operator, continuous 362
Operator, linear 361
Operator, stationary 362
Order of a distribution 46
Orthogonal polynomials see "Polynomials"
Oseen's equations 285 286
Output 360 ff
Parabolic axial distributions 299
Parseval's formula 137
Penny-shaped crack, capacity of 302
Penny-shaped crack, strain energy for 302
Periodic distributions 34
Plemelj formulas 31
Poisson distribution 392
Poisson's equation 187 287
Poisson's integral formula 256 281 337
Poisson's summation formula 153 154 168
Polarizability tensor, electric 308—310
Polarizability tensor, magnetic 308—310
Polarization potential 298 299
Polarization tensor 303—305
Polynomials, Bessel 390
Polynomials, Chebyshev 379
Polynomials, Hermite 375 377 387 388
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