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| Авторизация |
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| Hunter J.K., Nachtergaele B. — Applied Analysis |
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| Предметный указатель |
 -semigroup 114 163
 norm 4
 spaces 351
spaces, local 362
 norm 5
 -net 24
 -algebra 335
-algebra, Borel 336 338
-finite 337
Absolute convergence 8
Absolute convergence in a normed linear space 33
action 419
Activator 409
Adjoint of a bounded operator 193
Adjoint of an unbounded operator 246
Advection-diffusion equation 279
Airy's equation 329
Algebra 109
Almost everywhere 15 340
Almost periodic function 135
Analytic 220
Annihilation operator 147
Antilinear 126
Approximate identity 151
Approximate spectrum 241
Approximation scheme 114
Approximation scheme, consistent 114
Approximation scheme, convergent 114
Approximation scheme, stable 115
Arzela — Ascoli theorem 45
Asymptotically stable 235 404
Averaging kernel 260
Backwards heat equation 164
Baker — Campbell — Hausdorff formula 123
Ball, closed 14
Ball, open 14
Ball, unit 4
Banach algebra 39
Banach space 8 91
Banach space of linear operators 110
Banach — Alaoglu theorem 119 208
Banach — Steinhaus theorem 204
Base of open sets 84
Basis, Hamel 94
Basis, orthonormal 133
Basis, Schauder 94
Bernstein polynomials 40
Bessel function, spherical 279
Bessel's inequality 137
Bifurcation equation 425
Bifurcation theory 399
Biot — Savart law 284
Birkhoff ergodic theorem 204
Bolzano — Weierstrass theorem 23
Borel -algebra 336 338
Borel set 336
Born approximation 69
Boundary 88
boundary conditions 250
Boundary value problem 69 249
Bounded from above 9
Bounded from below 9
Bounded function 11
Bounded linear operator 95
Bounded linear transformation theorem 100
Bounded set 9
Brachistochrone problem 413
Brownian motion 327
Calculus of variations 410 420
Cantor function 32
Cantor set 16
Cartesian product 3
Cauchy sequence 7
Cauchy unordered sum 136
Cauchy — Schwarz inequality 128 357
Central limit theorem 320
Chain rule 388
Characteristic function of a random variable 323
Characteristic function of a set 343
Characteristic polynomial 217
Circle map 172
Classical solution 370
Closed ball 14
Closed operator 247
Closed set 15
Closure 16 88
Closure, sequential 86
Cluster point 31
Codimension 187 212
Coercive 34 211
Commutator 109
Compact metric space 25
Compact operator 110
Compact relatively 27
Compact resolvent 227
Compact support 39
Compact topological space 83
Complete measure space 339
Complete metric space 8
Complete metric space of continuous functions 38
Complete orthonormal set 139
Completion of a measure space 339
Completion of a metric space 19
Complex measure 337
Conjugate exponent, Sobolev 366
Conjugate linear 126
Connected 89
Continuous extension 100
Continuous function 12
Continuous in 376
Continuous random variable 320
Continuous spectrum 219
Continuous topological space 83
Continuous uniformly 13 27
Contraction 61
Contraction mapping theorem 62
Convergence of a sequence 6
Convergence of series 8
Convergence, absolute 8
Convergence, pointwise 35
Convergence, topological space 82
Convergence, unconditional 136
Convergence, uniform 36
Convergence, weak in Hilbert space 204
Convex function 209
Convex set 4
Convolution 150 298 359
Convolution operator 329
Convolution theorem 154 309
Countable 30
Countably additive 335
Counting measure 337
Covariance matrix of a Gaussian 330
Cover 24
Creation operator 147
Critical point 381 410
Cylinder set 85
d'Alembert's solution 185
Deficiency index 268
Delta function 253 291
Delta function, derivative of 296
Delta sequence 299
Dense 16
Derivative, distributional 295
Derivative, Frechet 386
Derivative, functional 415
Derivative, Gateaux 389
Derivative, variational 415
Derivative, weak 158 295 362
Devil's staircase 32
| Diagonal argument 46
Diagonalizable matrix 216
Diagonally dominant matrix 79
Diameter 11
Diffeomorphism 393
Differentiable 31
Differentiable map 386
Differential equation, existence and uniqueness 73 74
Differential equation, existence of solutions 53
Differential equation, nonlinear 52
Differential operator 249
Diffusion equation 161
Diffusion-driven instability 408
Dini's monotone convergence theorem 60
Dirac delta function 253
Direct method in the calculus of variations 381
Direct sum 133 187
Directional derivative 389
Dirichlet boundary conditions 250
Dirichlet form 270 372
Dirichlet kernel 183
Discrete Laplacian operator 240
Dispersive waves 170
Distance 11
Distance function 1
Distribution function 340
Distributional derivative 295
Distributions 287 294
Distributions, tempered 291
Divergent series 8
Domain of a linear operator 245
Domain regular 365
Dominated Convergence Theorem 348
du Bois — Reymond lemma 412
Dual basis 117
Dual space of 361
Dual space, algebraic 116
Dual space, topological 116
Duality pairing 293
Duhamel's formula 425
Dynamical system 63
Eigenvalue 216
Eigenvalue of a linear operator 219
Eigenvalue problem, Laplace's equation 277
Eigenvalue problem, Sturm-Liouville 268
Eigenvector 216
Energy norm 373
Epigraph 33
Equicontinuous 44
Equilibrium solution 380
Equivalence relation 33
Equivalent norms 101
Ergodic map 203
Ergodic theorem 172
Ergodic theorem, Birkhoff 204
Ergodic theorem, von Neumann's mean 201
Ergodic theorem, Weyl 173
Essential supremum 340
Essentially self-adjoint 248
Euclidean norm 4
Euclidean norm of a matrix 97
Euclidean space 4
Euler operator 415
Euler-Lagrange equation 412
Even function 156
Event 341
Exponential 112
Extended real numbers 342
Extension of an operator 246
Fatou's lemma 347
Fejer kernel 183
Final conditions 250
Finite element method 373
Finite part distribution 293
First countable 84
Fixed point 62 380
Flow 113
Fourier basis 134
Fourier coefficients 153
Fourier cosine expansion 156
Fourier series 149
Fourier sine expansion 156
Fourier transform 301
Fourier transform of a characteristic function 308
Fourier transform of a convolution 304
Fourier transform of a delta function 307
Fourier transform of a derivative 301
Fourier transform of a distribution 306
Fourier transform of a Gaussian 302
Fourier transform of a rotationally invariant function 330
Fourier transform of a Schwartz function 301
Fourier transform of a tempered distribution 306
Fourier transform of a translated function 304
Fourier transform of an exponential function 308
Fourier transform of positive type 329
Fourier transform on 307
Fourier transform on  311
Fourier transform, eigenfunctions 312
Fourier transform, inverse transform 305
Fourier — Laplace transform 310
Fractal 16
Fredholm alternative 195
Fredholm integral equation 67
Fredholm integral operator 68
Fredholm operator 196
Free boundary conditions 416
Freshet derivative 386
Freshet space 289
Fubini's theorem 350
Function even, odd 156
Function of an operator 232
Functional 116
Functional calculus 232
Functional derivative 415
Functional, linear, on Hilbert space 190
Fundamental lemma of the calculus of variations 412
Fundamental theorem of calculus 384
Gamma function 276
Gateaux derivative 389
Gauss — Seidel method 79
Gaussian 302 321 341
Generalized Holder inequality 375
Generator 114
Gibbs phenomenon 155
Gradient 425
Gradient flow 77
Gradient mapping 417
Gram — Schmidt procedure 140
Graph of an operator 248
Green's function 70 245 253 254 316
Green's function of Laplace's equation 276
Green's function of the heat equation 163
Green's theorem 250 274
Gronwall's inequality 56
Haar measure 339
Haar scaling function 176
Haar wavelet basis 177
Hahn — Banach theorem 118
Hamel basis 94
Hamiltonian operator 147
Hamiltonian system 77 419
Hardy's inequality 284
Harmonic map 423
Hausdorff 82
Heat equation 69 161
Heat equation, Green's function 318
Heat equation, smoothing property 318
Heaviside step function 254
Heine — Borel theorem 23
Heisenberg uncertainty principle 332
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