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| Stakgold I. — Green's Functions and Boundary Value Problems |
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| Предметный указатель |
Abel's formula for the Wronskian 187
Absolutely continuous functions 307 532
Action of distribution 91
Adjoint for unbalanced problem 206 214
Adjoint, boundary conditions 198
Adjoint, boundary value problem 198
Adjoint, formal 100 167 170
Adjoint, Green's function 200
Adjoint, matrix 208
Adjoint, operator 313
Admissible pair 315
Algebraic independence 228 268 290
Alternative theorems for boundary value problems 210
Alternative theorems for integral equations 210 337
Alternative theorems in Euclidean space 208 321 323
Angular current density 26
Angular density 25
Arondszajn, N. 398
Arrhenius law 4 9
Ball, closed 1
Ball, open 1
Banach space 261
Band-limited functions 145 348 385
Base problem 566 591 594
Basis 228 297
Basis, dual 293
Basis, orthonormal 277 281—290 297
Basis, reciprocal 293
Basis, Schauder 277
Bazley, N.W. 348
Beam 63 70 83 553—557
Bessel equation 439 448
Bessel equation, modified 77
Bessel functions 288
Bessel's inequality 128 281
Bifurcation see "Branching"
Bihaimonic operator 559
Bilinear form 274
Bilinear form, associated quadratic form 275
Bilinear form, coercive 525
Bilinear form, nonnegative 525
Bilinear form, positive 525
Bilinear form, symmetric 525
Blow-up 630
Boas, R.P. 122
Bolzano — Weierstrass theorem 335
Boundary 2
Boundary conditions for heat conduction 6
Boundary conditions in limit-circle case 447
Boundary conditions in recycling 13
Boundary conditions, adjoint 198 205
Boundary conditions, essential 535
Boundary conditions, for beam 18
Boundary conditions, natural 535 559
Boundary conditions, periodic 427 503
Boundary conditions, unilateral 536
Boundary conditions, unmixed 192
Boundary functional 192 204
Boundary value problems for second order equations 192
Boundary value problems, for equations of order p 203
Boundary value problems, regular 412
Boundary value problems, singular 412 438
Branch, Branch-point 583
Branching 575 582—591 603
Branching from infinity 618
Buckling 569
Capacity 550
Catastrophe theory 587
Cauchy data, Cauchy problem 469
Cauchy sequence see "Fundamental sequence"
Cesaro sums 136 143
Characteristics 182 470
circle 1
Closed set 240
Closure 2 239
Codimension 309
Collision cross section 25
Compact operators 335 357
Compact set 240
Comparison theorem for diffusion 497
Compatibility see "Solvability conditions"
completely continuous see "Compact operators"; "Compact set"
Completeness relation 139
Conjunct 167
Connected 2
Consistency see "Solvability conditions"
Constitutive relations 19
Continuous dependence for diffusion 497
Continuous dependence for wave equation 501
continuous dependence on data 57
Contraction 244 488
Convergence in space of test functions 89 154
Convergence of sequence of reals 31
Convergence, Cauchy criterion for 31
Convergence, distributional 107
Convergence, mean (or  ) 34
Convergence, mean square (or  ) 35 283
Convergence, pointwise 31 283
Convergence, uniform 32
Convergence, weak 339
Convex set 268 555
Convolution 104 163 363
DATA 42
Deficiency 325
Delta sequence 110 284
Dense set 240
Dependence and independence 186 227
Differential inequalities 64
Diffusion 71 73
Diffusion equation 7 475
Diffusion operator 170
Diffusion-reaction 612—621
Diffusivity 8
Dipole 509
Dipole layer see "Double layer"
Dirac delta function 53
Dirichlet function 38
Dirichlet integral 561
Dirichlet kernel 113 114 121 133
Dirichlet problem 501—507 513—517
Dirichlet problem for disk 113
Dirichlet problem, exterior 515 550
Disk 1
Distance function see "Metric"
Distributions 86—184
Distributions of slow growth 154
Distributions, action of 91
Distributions, complex-valued 137
Distributions, convergence of 107
Distributions, coordinate transformation of 120
Distributions, differentiation of 97
Distributions, dipole 95 97
Distributions, Dirac 94 98
Distributions, direct product of 122
Distributions, parametric differentiation of 115
Distributions, regular 93
Distributions, singular 93
Distributions, translation of 94
Domain 2 45
Domain of dependence 486—488
Domain of function or operator 222 295
Domain perturbation 599
Domination 66 497
Double layer 116 510
Drift 498
Duhamel's formula 45 488
Eigenfunctions 60
Eigenfunctions of compact, self-adjoint operator 373
Eigenfunctions, basis of 331
Eigenvalues 60 324 332
| Eigenvalues of compact operators 357
Eigenvalues, degenerate 334
Eigenvalues, estimation of 392—409
Eigenvalues, geometric multiplicity of 325 357
Eigenvectors 324
Elements of finite energy 528
Energy inner product 524 525 537 554
Energy norm 524 525 537
Equality almost everywhere 92
Error function 457
Euclidean space 264
Euler — Bernoulli law 571
Euler — Lagrange equation 524
Expansion theorem 372
Fejer kernel 112 143
Finite part of divergent integrals 102 106
Fission 27
Fixed points 243 563 596
Forced problem 583
Forcing function 42
Fourier coefficients 128 279
Fourier integral theorem 145
Fourier series of distributions 137
Fourier series, convergence of 132
Fourier series, convolution 143 384
Fourier series, Dirichlet conditions for 130
Fourier series, full-range 287
Fourier series, general 281
Fourier series, half-range 287
Fourier series, mean-square convergence of 128
Fourier sine transform 453
Fourier sum 279
Fourier transform 140 144 148 365 462
Fourier — Bessel series 450
Fourier's law 3
Fox, D.W. 398
Frechet derivative 579
Fredholm alternative see "Alternative theorems"
Fredholm integral equations 247 248 356
Fredholm integral equations of potential theory 514 516
Friedrichs' inequality 537
Functionals 87 224
Functionals, bounded 291
Functionals, continuous 291
Functionals, critical point of 580
Functionals, linear 290
Functionals, norm of 291
Functionals, quadratic 525
Functionals, stationary 525
Functions of slow growth 1 52
Fundamental sequence 31 234
Fundamental solution, casual 178 180 484 485 see
Fundamental solution, pole of 177
Galerkin equation 395 540
Gauss kernel 113
Generalized functions see "Distributions"
Gibbs phenomenon 134
Gradient operator 580
Gram — Schmidt process 268
Green's formula 168 169
Green's function 43 194 259 see
Green's function for Bessel's equation 423 462
Green's function for diffusion 488 493
Green's function for first-order BVP 431
Green's function for periodic problem 428
Green's function for semi-infinite strip 454
Green's function for unit disk 506
Green's function for wave equation 485
Green's function in limit-circle case 444
Green's function in limit-point case 441
Green's function, adjoint 200
Green's function, bilinear series 61 415
Green's function, causal 69
Green's function, direct 200
Green's function, modified 215 217 520
Green's function, relation to eigenfunctions 416
Hankel transform 459
Harmonic functions 502
Harmonic functions, maximum principle for 66 507
Harmonic functions, mean value theorem for 507
Heat conduction 2 See
Heaviside function 47 93 159
Heisenberg's uncertainty principle 146
Hermite equation 439
Hermite polynomials 288 391
Hilbert space 263
Hilbert space, separable 276
Hilbert — Schmidt kernels see "Kernel"
Hyperbolic equations 475 482—488
Images 72 459 491 493
Indicator function 93 100
Infimum 2
Initial value problem 68 186
Inner product 208 261 262
Inner product space, complex 262
Inner product space, real 261
Integral equations 61 210 247
Integral equations for capacity 552
Integral equations for Dirichlet problem 513—517
Integral equations, Abel 347 390
Integral equations, eigenvalue problem for 369
Integral equations, Fredholm 247 248 356
Integral equations, inhomogeneous 378—391
Integral equations, Volterra 249 388
Integral operator 248 300 351
Integral operator, Hammerstein 577
Integral operator, Hilbert — Schmidt 352
Integrodifferential equations 28 405—409 560
Interface condition 78 81 82
Jensen's inequality 631
Jordan — von Neumann theorem 274
Kernel 248 300
Kernel, bilinear expansion of 276
Kernel, difference 367 384
Kernel, Hilbert — Schmidt 300 352 360 447
Kernel, Holmgren 303 352 362 443
Kernel, iterated 355
kernel, Poisson 113 121 122 384
kernel, resolvent 382
Kernel, separable 352
Kohn — Kato method 402
Lagrange identity 168 169
Landau, H.J. 387
Laplace transform 163 487
Laplace's equation 176 475 481 502—520 See
Laplacian 44 169
Least squares 558
Lebesgue dominated convergence theorem 33 34 40
Lebesgue integral 36
Legendre equation 440
Legendre polynomials 271 286
Level line coordinates 548 560
Lewis number 12
Liapunov — Schmidt method 605
Limit-circle 437 438 444
Limit-point 437 438 440
Linear dependence see "Dependence and independence"
Linear independence see "Algebraic independence"; "Dependence and independence"
Linear manifold 229 264
Linear space 226
Linear space, basis for 228
Linear space, complex 226
Linear space, dimension of 228
Linear space, normed 259
Linear space, real 226
Linearization 578
Lipschitz continuous 244 247 249
Locally integrable 91
Macdonald function 462
Mapping see "Transformations"
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