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| Ïîèñê ïî óêàçàòåëÿì |
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| Stakgold I. — Boundary value problems of mathematical physics |
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| Ïðåäìåòíûé óêàçàòåëü |
Addition theorem for cylindrical waves 268
Addition theorem for Legendre functions 398
Addition theorem for spherical waves 290
Adjoint 9 198
Admissible functions 332
Approximation in subspace 335—336
Aronszajn, N. 382
Asymptotic expansions for heat equation 206 222 236
Asymptotic expansions of eigenvalues of Laplacian 231—234 239—240
Asymptotic expansions of integrals 399—402
Base operators 382
Bazley, N.W. 382
Bessel equation 242 268—270 295
Biharmonic equation 40 105 365
Boundary conditions, essential 353
Boundary conditions, natural 352—355
Boundary value problem 88
Boundary value problem, well-posed 89
Capacity 171—174 350—352
Cauchy data 74
Cauchy problem 73
Causal function see "Right-sided function"
Causal fundamental solution see "Fundamental solution"
Characteristic 74
Characteristic of wave equation 46
Characteristic, surface 74
Classification of partial differential equations 73—87
Comparison theorem 377
Composite medium 183 234—293
Conductor 171—183
Consistency condition 171
continuous dependence on data 89 91 95 102—103 226
Convolution 18—20 49
Cylindrical wave 267—268
d'Alembert's formula 85
Damped wave equation 65—69 257—259 264
Delta function 5 20 27 34
Descent, method of 255
Diaz, J. 344
Difference kernel 311
Diffraction see "Scattering"
Diffusion 230 240—241 329 see
Dipole 6 111 201
Dipole layer 12 113
Dirichlet problem 90—103 122—125 135 142 172 296 348
Dissipative wave equation see "Damped wave equation"
Distributions of slow growth 31 37
Distributions, action of 4
Distributions, convergence of 10—16
Distributions, convolution of 18
Distributions, definition of 4 31 37
Distributions, differentiation of 7
Distributions, dipole 6 8
Distributions, Dirac 5
Distributions, direct product of 17
Distributions, partial differential equations for 39
Distributions, product of functions and 7
Distributions, regular 5
Distributions, singular 5
Distributions, translation of 5
Distributions, values of 9
Divergence theorem 89
Eigenfunction expansion for heat-conduction equation 213—218
Eigenfunction expansion for Laplace's equation 153—164
Eigenfunction expansion for wave equation 248 252
Eigenvalues of negative Laplacian 136—142
Eigenvalues, asymptotic distribution of 231 239—240
Eigenvalues, comparison theorem for 377
Eigenvalues, extremal principles for 369—392
Eigenvalues, lower bounds to 381—392
Elliptic equations 80
Energy flux 262 303
Energy inner product 342
Energy integral for heat conduction 225
Energy integral for wave equation 244 261—262
Energy norm 343
Entire functions 315
Extremal principles for capacity 350—352
Extremal principles for eigenvalues in Hilbert space 372—392
Extremal principles for eigenvalues in n space 369—372
Extremal principles for functional 337—340 352—355 358—361
Extremal principles for torsional rigidity 346—348
Extremal principles, complementary 344—352
Fluid flow 185—190
Fokker — Planck equation 230
Fourier integral theorem 23
Fourier transforms and Wiener — Hopf equations 311—331
Fourier transforms of distributions 30—39
Fourier transforms of functions 23
Fourier transforms of test function 31
Fox, D.W. 382
Free boundary 237
Friedrichs, K.O. 344
Functionals 3 332
Functionals, continuity of 3
Fundamental solution 48
Fundamental solution of damped wave equation 65—69
Fundamental solution of heat-conduction equation 58—60 198
Fundamental solution of Helmholtz's equation 53—58 266—267
Fundamental solution of Laplace's equation 49—53
Fundamental solution of wave equation 61—65 249 253—256
Fundamental solution on Riemann surface 270—272
Fundamental solution, pole of 48
Generalized functions see "Distributions"
Generalized solution 42
Green's function see also "Fundamental solution"
Green's function for heat conduction 198 204 209—218
Green's function for Helmholtz's equation 265—290
Green's function for Laplace's equation 130—171
Green's function for wave equation 246—252
Green's theorem 40 89
Hadamard, J. 255
Hankel functions see "Bessel equation"
Hankel transform 275—280
Harmonic functions, maximum principle for 101
Harmonic functions, mean value theorem for 99
Heat-conduction equation 81 194—243 280—281
Heat-conduction equation in composite medium 234—237
Heat-conduction equation, backward 229
Heat-conduction equation, causal fundamental solution 58—60
Heat-conduction equation, causal Green's function for 197—222
Heat-conduction equation, energy integral for 223
Heat-conduction equation, Green's theorem for 41 196
Heat-conduction equation, ill-posed problems for 229
Heat-conduction equation, maximum principle for 224—225
Heat-conduction equation, Stefan problem for 237—238
Heat-conduction equation, uniqueness for 225—226
Helmholtz's equation in exterior domain 294—311
Helmholtz's equation in wedge 272—273
Helmholtz's equation, fundamental solution of 53—58
Helmholtz's equation, Green's function for 265—285
Helmholtz's equation, half-plane problem for 281—290 321—327
Helmholtz's equation, mean value property 105
Hilbert — Schmidt kernels 135 375
Huyghens' principle 256
Hyperbolic equations 80—85
Images 149 166—169 204 209 211 251 252
Incident field 299
Initial data 72
Initial value problem 73
Integral equations for capacity 172—174 351
Integral equations for scattering problems 301
Integral equations of potential theory 122—130 146 171—193
Integral equations of Wiener — Hopf type 311—331
| Integral equations with difference kernel 311—331
Integrodifferential equation 366—367 389—390
Interior operator 74
Intermediate problems 382
Jones, D.S. 368
Kantorovich — Lebedev transform 273
Kirchhoff's formula 263
Klein — Gordon equation 70
Laplace transform 38 206 218 236 249 401—402
Laplace's equation 40 49—53 88—192 see
Laplace's equation in two dimensions 128
Laplace's equation, eigenvalue problem for 136—142 231—234
Laplace's equation, exterior Dirichlet problem for 123 129 142
Laplace's equation, fundamental solution of 49—53
Laplace's equation, Green's function for 130—171
Laplace's equation, Green's theorem for 40
Laplace's equation, interior Dirichlet problem for 122 128 135
Laplace's equation, Neumann problem for 126 128
Layers, double 12 113
Layers, simple 7 39 112
Layers, surface 7 12 110—121
Least squares 361—363
Left-side function 28
Legendre functions 393—398
Levine, H. 283 311 340 357
Limiting absorption 259—261
Locally integrable 2
Macdonald function 266 279 321
Mapping function 164
Maximin theorem 371
Maximum Principle for harmonic functions 101
Maximum principle for heat conduction 224
Maximum theorem for functionals 337
Mean value property for biharmonic equation 105
Mean value property for Helmholtz equation 105
Mean value property of harmonic functions 99
Mehler's integral representation 284
Mellin transform 167 169
Minimax theorem 371
Monochromatic excitation 259—261
Multiindex 2
Neumann problem 126 128 171 185—191
Neumann problem and fluid flow 185—191
Neumann problem, consistency condition for 171
Neumann problem, extremal principles for 363—364
Null sequences 3 30 36
One-sided functions 28
Operators, base 382
Operators, bounded above 372
Operators, bounded below 372
Operators, completely continuous 133—135 375
Operators, Hilbert — Schmidt 135 375
Operators, indefinite 355—357
Operators, integrodifferential 366 389—390
Operators, interior 74
Operators, nonnegative 336
Operators, nonsymmetric 355—357
Operators, positive 337 358
Operators, self-adjoint 9 376
Operators, semibounded 372
Operators, strongly positive 343 363
Operators, symmetric 337
Parabolic equations 80
Parseval formula 24
Partial differential equations 88—311
Partial differential equations for distributions 39—48
Partial differential equations of first order 76—79
Partial differential equations of second order 79—87
Partial differential equations, classification of 73—87
Partial differential equations, elliptic 80
Partial differential equations, fundamental solutions of 48—72
Partial differential equations, hyperbolic 80
Partial differential equations, parabolic 80
Plane wave 285—286 302
Poisson equation 103 345
Poisson kernel 95
Poisson sum formula 212
Pole of fundamental solution 48
Potential theory 88—193 267 see
Projection operator 335—336
Propagation of discontinuities 46 77
Radiation condition 297
Rayleigh quotient 369
Rayleigh — Ritz procedure see "Ritz — Rayleigh"
Reciprocity principle 303 342 368
Rellich, F. 297
Retarded potential 254
Riemann mapping theorem 164
Riemann surface 270
Right-side function 28
Ritz — Rayleigh, equations 341 363 366—368
Ritz — Rayleigh, procedure 332 334 340—343 362 377—378
Scattered amplitude 304
Scattered field 300
Scattering 299—311 328
Scattering cross section 303
Scattering cross section, stationary principle for 309
Schwarz constants 380
Schwarz inequality 344
Schwinger — Levine principle 311 340 357
Self-adjoint 9 376
Semigroups of operators 227
Slow growth, distribution of 31 37
Slow growth, functions of 29
Sokolnikoff, I.S. 346
Sommerfeld, A. 277 297
Spherical harmonics 109 126 127 144 290 295 393—398
Spherical wave 267 290
Stationary principles for indefinite operators 356
Stationary principles for nonsymmetric operators 357 367—368
Stationary principles for scattering cross section 309—311
Steady heat conduction 88 183
Stefan Problem 237
Strict solution 42
Support 2
Symbolic functions see "Distributions"
Tangential derivative 74
Telegraphy equation 65 258
Test functions 3
Test functions of rapid decay 30 36
Test functions, convergence of 3 30
Test functions, null sequences of 3 30 36
Theta function 212
Torsional rigidity 346—348
Transversal 41
Uniqueness theorem for heat conduction 225—226
Uniqueness theorem for Helmholtz's equation 296—299
Uniqueness theorem for Laplace's equation 102
Uniqueness theorem for wave equation 243
variation-iteration 380—381
Variational methods see "Extremal principles" "Stationary
Wave equation 81 194 196—197 243—265 289—294
Wave equation in composite medium 293
Wave equation, d'Alembert's solution of 85
Wave equation, damped 65—69 257—259 264
Wave equation, fundamental solution of 61—65
Wave equation, generalized solution of 44
Wave equation, Green's function of 246—256
Wave equation, Green's theorem for 41 47 197
Wave equation, method of descent for 255—256
Wave guide 291
Weber transform 242
Weinstein, A. 382
Well-posed problem 89
Wiener — Hopf equation 311—331
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