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| Авторизация |
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| Hunter J.K., Nachtergaele B. — Applied Analysis |
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| Предметный указатель |
Hermite functions 272
Hermite polynomials 146
Hermitian 197
Hessian matrix 417
Hilbert cube 230
Hilbert space 126
Hilbert space, separable 133
Hilbert transform 316
Hilbert — Schmidt integral operator 231
Hilbert — Schmidt matrix norm 98 127
Hilbert — Schmidt operator 230
Hodograph method 396
Hoelder continuous 181 267 367
Hoelder's inequality 356
Holomorphic 220
Holonomic constraint 423
Homeomorphism 83
Homogenized equation 286
Hopf bifurcation 405
Ill-posed 104 164 185
Implicit function theorem 393
Independent random variable 321
Index of Fredholm operator 196
Indicator function 323
Indirect method in the calculus of variations 381
Inequality, Cauchy-Schwarz 357
Inequality, generalized Holder 375
Inequality, Gronwall's 56
Inequality, Hardy's 284
Inequality, Hoelder 356
Inequality, isoperimetric 170
Inequality, Jensen 355
Inequality, Poincare 369 370
Inequality, Tchebyshev 359
Inequality, triangle for  norm 358
Inequality, Young's 359
Inequalitym Minkowski 358
Infimum 9 28 29
Inhibitor 409
Initial value problem 52
Inner product 125
Inner product space 125
Inner product, standard 126
Integrable function 345
Integral, Lebesgue 344
Integral, Riemann 382
Interior 88
Interpolation inequality 376
Invariant subspace 222
Inverse function theorem 380 393
Isometric embedding 18
Isometry 18
Isomorphic Hilbert spaces 133 199
Isomorphic metric spaces 18
Isoperimetric constraint 422
Isoperimetric inequality 170
Jacobi theta function 319
Jacobi's method 79
Jacobian 396
Jacobian matrix 387
Jensen's inequality 355
KdV equation 169 242
Kernel 102
Kronecker delta function 117
Ladder operator 147
Lagrange multiplier 421
Lagrangian 410
Laplace transform 310 385
Laplace — Beltrami equation 278
Laplace's equation 168 273 370
Laplace's equation, eigenvalue problem 277
Laplace's equation, Green's function 276
Lax pair 242
Lax — Milgram lemma 373 376
Lebesgue dominated convergence theorem 348
Lebesgue integral 344
Lebesgue measure 338
Lebesgue — Stieltjes integral 346
Lebesgue — Stieltjes measure 340
Legendre functions 272
Legendre polynomials 145 272
Legendre transform 417 418
Liapounov function 77 404
Liapounov — Schmidt reduction 425
Limit cycle 405
Linear asymptotic stability 404
Linear form 116
Linear functional 116
Linear functional on Hilbert space 190
Linear operator 95
Linear operator, unbounded 245
Linear spaces, finite-dimensional 106
Linear stability 404
Linear subspace 5
Lipschitz continuous 48 73
Local space 362
Locally convex space 289 328
Lower bound 9
Lower semicontinuous 14
Lower semicontinuous, weakly 209
Maximum 10 28
Maximum norm 5
Maximum principle 72
Mazur's theorem 210
Mean ergodic theorem 201
Mean of a function 355
Mean of a random variable 321
Mean value theorem 32 385
Measurable function 341
Measurable set 335 336
Measure 335
Measure preserving map 202
Measure space 337
Measure theory 335
Measure zero set 15 339
Measure,  -finite 337
Measure, complex-valued 337
Measure, counting 337
Measure, definition of 336
Measure, Lebesgue 338 340
Measure, signed 337
Measure, vector-valued 337
Method of images 331
Metric 1
Metric space 2
Metric space, complete 8
Metrizable topological space 85
Minimum 10 28
Minkowski's inequality 358
Mixed boundary conditions 250
Modified Green's function 258
Modified Newton's method 401
Mollifier 260
Monotone 10
Monotone Convergence Theorem 347
Monotone convergence theorem, Dini's 60
Monte Carlo method 175
Multi-index 287
Multiplicity 218
Multiresolution analysis 179
Natural boundary conditions 416
Navier — Stokes equations 212
Neighborhood 17 82
Neighborhood base 84
Nemitski operator 392
Nets 85
Neumann boundary conditions 250
Neumann series 69
Neumann, von mean ergodic theorem 201
Newton's method 400
| Nilpotent matrix 122
Nilpotent operator 221
Noether's theorem 414
Nonlinear ODE 52
Nonnegative operator 198
Nonsingular linear map 95
Norm 4
Norm,  4
Norm,  5
Norm, equivalent 101
Norm, Euclidean 4
Norm, Hilbert-Schmidt 230
Norm, maximum 5
Norm, operator 95
Norm, sum 4
Norm, supremum 36
Norm, uniform 36 95
Normal matrix 217
Normal operator 201
Null Lagrangian 416
Null space 102
Nullity 102
Odd function 156
ODE, blowup 52
ODE, existence and uniqueness 73 74
ODE, existence of solutions 53
ODE, nonlinear 52
ODE, uniqueness theorem 57
Open ball 14
Open cover 24
Open mapping theorem 101
Open set, metric spaces 15
Open set, topological spaces 81
Operator, bounded 95
Operator, bounded from below 198
Operator, closable 248
Operator, closed 247
Operator, compact 110
Operator, differential 249
Operator, functions of 232
Operator, Hilbert — Schmidt 230
Operator, self-adjoint 247
Operator, Sturm-Liouville 252
Operator, symmetric 247
Operator, topology 109
Operator, trace class 231
Operator, unitary 199
Orbit 172
Orthogonal 199
Orthogonal complement 130
Orthogonal direct sum 133
Orthogonal projection 188
Orthogonal set 133
Orthogonal vectors 130
Orthonormal basis 133 139
Oscillatory integral 330
Parallelogram law 129
Parseval's identity 139
Partial derivative of a map 392
Payley — Weiner theorem 310
Peano existence theorem 58
Periodic boundary conditions 250
Picard existence theorem 58
Pitchfork bifurcation 399
Poincare inequality 184 369 370
Point spectrum 219
Pointwise convergence 343
Pointwise-a.e. convergence 343
Poisson distribution 341
Poisson kernel 169
Poisson summation formula 319
Polar decomposition 217
Polarization 129
Polynomial growth 294
Polynomial, Bernstein 40
Polynomial, Hermite 146
Polynomial, Legendre 145 272
Polynomial, Tchebyshev 146
Polynomial, trigonometric 150
Population dynamics 64
Positive definite operator 198
Positive operator 198
Power set 82
Pre-Hilbert space 125
Precompact 27
Precompact, subset of Hilbert space 228
Principal value distribution 293
Probability measure 340
Probability space 340
Product -algebra 349
Product measure 349
Projection 187 188
Projection theorem 130
Pseudo-differential operator 316
Quasiperiodic 134
Quotient space 211
Random variable 142 320 342
Random variable, Gaussian 321
Random walk 322
RANGE 102
Rank 102
Reaction-diffusion equation 406
Reflection operator 297
Reflexive Banach space 119
Regular distribution 292
Regular domain 365
Regular point 381
Regular Sturm — Liouville problem 271
Regulated functions 382
Rellich — Kondrachov theorem 368
Rellich's theorem 266
Residual spectrum 219
Residual spectrum of a self-adjoint operator 224
Resolvent equation 239
Resolvent operator 219 220
Resolvent set 218
Resonance 398
Restriction of an operator 246
Riemann integral 382
Riemann — Lebesgue lemma 308
Riesz representation theorem 191
Riesz transform 316
Right shift 240
Rotation map 172
Sample space 341
Schauder basis 94
Schauder fixed point theorem 62
Schwartz function 288
Schwartz space 287 288
Secant method 78
Second-order random variable 143
Self-adjoint boundary conditions 247 251
Self-adjoint boundary value problem 251
Self-adjoint operator 197 247
Semicontinuous 14
Seminorm 289
Separable spaces 354
Separable Hilbert space 133
Separable metric space 17
Sequence, Cauchy 7
Sequence, convergent 6
Sequence, divergent 6
Sequentially compact metric space 23
Series 7 33
Series, uncountable 136
Sesquilinear 126
Shift operator 103
Shift operator, spectrum 240
Sign function 97
Signed measure 337
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