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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—36
Aronszajn, N. 382
Asymptotic expansions for heat equation 206 222 236
Asymptotic expansions of eigenvalues of Laplacian 231—34
Asymptotic expansions of integrals 399—402
Asymptotic expansions, 239—40
Base operators 382
Bazley, N.W. 382
Bessel equation 242 268—70 295
Biharmonic equation 40 105 365
Boundary conditions, essential 353
Boundary conditions, natural 352—55
Boundary value problem 88
Boundary value problem, well-posed 89
Capacity 171—74 350—52
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—83
Consistency condition 171
continuous dependence on data 89 91
Continuous dependence on data, 95 102—103 226
Convolution 18—20 49
Cylindrical wave 267—68
Damped wave equation 65—69 257—59
Damped wave equation, 264
Delta function 5 20 27 34
Descent, method of 255
Diaz, J. 344
Difference kernel 311
Diffraction (see “Scattering”)
Diffusion 230 240—41 329
Dipole 6 111 201
Dipole layer 12 113
Dirac 5
Dirac of slow growth 31 37
Dirac, direct product of 17
Dirac, partial differential equations for 39
Dirac, product of functions and 7
Dirac, regular 5
Dirac, singular 5
Dirac, translation of 5
Dirac, values of 9
Dirichlet problem 90—103 122—25 135 142 172 296 348
Dissipative wave equation (see “Damped wave equation”)
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
Divergence theorem 89
D’Alembert’s formula 85
Eigenfunction expansion for heat-conduction equation 213—18
Eigenfunction expansion for Laplace’s equation 153—64
Eigenfunction expansion for wave equation 248 252
Eigenvalues of negative Laplacian 136—42
Eigenvalues, asymptotic distribution of 231 239—40
Eigenvalues, comparison theorem for 377
Eigenvalues, extremal principles for 369—92
Eigenvalues, lower bounds to 381—92
Elliptic equations 80
Energy flux 262 303
Energy inner product 342
Energy integral for heat conduction 225
Energy integral for wave equation 244 261—62
Energy norm 343
Entire functions 315
Extremal principles for capacity 350—52
Extremal principles for eigenvalues in Hilbert space 372
Extremal principles for eigenvalues in n space 369—72
Extremal principles for functionals 337 40 352—55 358-361
Extremal principles for torsional rigidity 346—48
Extremal principles, 392
Extremal principles, complementary 344—52
Fluid flow 185—90
Fokker — Planck equation 230
Fourier integral theorem 23
Fourier transforms and Wiener — Hopf equations 311—31
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
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—56
Fundamental solution, on Riemann surface 270—72
Fundamental solution, pole of 48
Generalized functions (see “Distributions”)
Generalized solution 42 (see also “Fundamental solution”)
Green’s function; see also Fundamental for heat conduction 198 204 209—18
Green’s function; see also Fundamental for Helmholtz’s equation 265—90
Green’s function; see also Fundamental for Laplace’s equation 130—71
Green’s function; see also Fundamental for wave equation 246—52
Green’s Theorem 40 89
Hadamard, J. 255
Hankel functions (see “Bessel equation”)
Hankel transform 275—80
Harmonic functions, maximum principle for 101
Harmonic functions, mean value theorem for 99
Heat-conduction equation 81 194—243
Heat-conduction equation, 280—81
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, in composite medium 234—37
Heat-conduction equation, maximum principle for 224—25
Heat-conduction equation, Stefan problem for 237—38
Heat-conduction equation, uniqueness for 225—26
Helmholtz’s equation, fundamental solution of 53—58
Helmholtz’s equation, Green’s function for 265—85
Helmholtz’s equation, half-plane problem for 281—90 321—27
Helmholtz’s equation, in exterior domain 294—311
Helmholtz’s equation, in wedge 272—73
Helmholtz’s equation, mean value property 105
Hilbert — Schmidt kernels 135 375
Huyghens’ principle 256
Hyperbolic equations 80—85
Images 149 166—69 204 209 211 251
Images, 252
Incident field 299
Initial data 72
| Initial value problem 73
Integral equations for capacity 172—74 351
Integral equations for scattering problems 301
Integral equations of potential theory 122—30 146 171
Integral equations of Wiener — Hopf type 311—31
Integral equations with difference kernel 311—31
Integral equations, 193
Integrodifferential equation 366—67 389-390
Interior operator 74
Intermediate problems 382
Jones, D. S. 368
Kantorovich — Lebedev transform 273
Kirchhoif s formula 263
Klein — Gordon equation 70
Laplace’s equation 40 49—53 88—192
Laplace’s equation, eigenvalue problem for 136—42 231
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—71
Laplace’s equation, Green’s theorem for 40
Laplace’s equation, interior Dirichlet problem for 122 128
Least squares 361—63
Left-side function 28
Legendre functions 393—98
Levine, H. 283 311 340 357
Limiting absorption 259—61
Locally integrable 2
Macdonald function 266 279 321
Mapping function 164
Maximin theorem 371
Mehler’s integral representation 284
Mellin transform 167 169
Minimax theorem 371
Monochromatic excitation 259—61
Multiindex 2
Neumann problem 126 128 171 185
Neumann problem and fluid flow 185—91
Neumann problem for 126 128
Neumann problem for, double 12 113
Neumann problem for, in two dimensions 128
Neumann problem for, Laplace transform 38 206 218 236
Neumann problem for, simple 7 39 112
Neumann problem for, surface 7 12 110—121
Neumann problem, consistency condition for 171
Neumann problem, extremal principles for 363—64
Null sequences 3 30 36
One-sided functions 28
Operators, base 382
Operators, bounded above 372
Operators, bounded below 372
Operators, completely continuous 133—35 375
Operators, Hilbert — Schmidt 135 375
Operators, indefinite 355—57
Operators, integrodifferential 366 389—90
Operators, interior 74
Operators, nonnegative 336
Operators, nonsymmetric 355—57
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—86 302
Poisson equation 103 345
Poisson kernel 95
Poisson sum formula 212
Pole of fundamental solution 48
Potential theory 88—193 267
Projection operator 335—36
Propagation of discontinuities 46 77
Radiation condition 297
Rayleigh quotient 369
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—68
Ritz — Rayleigh, procedure 332 334 340—43 362 377-378
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
Spherical harmonics, 290 295 393—98
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—11
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—48
Transversal 41
Uniqueness theorem for heat conduction 225—26
Uniqueness theorem for Helmholtz’s equation 296—99
Uniqueness theorem for Laplace’s equation 102
Uniqueness theorem for wave equation 243
Variation-iteiation 380—81
Variational methods (see Extremal principles and Stationary principles)
Wave equation 81 194 196—97 243—65
Wave equation, damped 65—69 257—59 264
Wave equation, d’Alembert’s solution of 85
Wave equation, fundamental solution of 61—65
Wave equation, generalized solution of 44
Wave equation, Green’s function of 246—56
Wave equation, Green’s theorem for 41 47 197
Wave equation, in composite medium 293
Wave equation, method of descent for 255—56
Wave guide 291
Weber transform 242
Weinstein, A. 382
Well-posed problem 89
Wiener — Hopf equation 311—31
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