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Kanwal R.P. — Generalized functions: Theory and technique
Kanwal R.P. — Generalized functions: Theory and technique

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Название: Generalized functions: Theory and technique

Автор: Kanwal R.P.

Аннотация:

Contains both the theory and applications of generalized functions with a significant feature being the quantity and variety of applications. New updated edition. DLC: Theory of distribution (Functional analysis)


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 443

Добавлена в каталог: 30.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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