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| Авторизация |
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| Поиск по указателям |
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| Cohen G.L. — A Course in Modern Analysis and Its Applications |
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| Предметный указатель |
![$C^{'}[a, b]$](/math_tex/6c13b0c8d06595ea9d7cf14bf1cfb47982.gif) 246
![$C^{(1)}[a, b]$](/math_tex/4fa4413805533000f1d7d64791a0115b82.gif) 74
![$C^{w}[a, b]$](/math_tex/1ac7b022ed3436a987579952aa13408d82.gif) 265
![$C_{1}[a, b]$](/math_tex/6d522efaf087b676df5e0d30b4156a6a82.gif) 94 178
![$C_{2}[a, b]$](/math_tex/05ccc5e28b6731f830242c451872905b82.gif) 94 178 255
 92
 90 175 177 255
 92
 -space 173
 19
 -neighbourhood 20
 -net 152
 19
 8 72 80 90 177 254
 5
 5 17
 ,  5 17
 8 72 80 87 177 254
 5
Absolute value 4 54
Adjoint 285
Annihilator 279
Approximation theory 149 192 280 283
Arzela 148
Ascoli's theorem 146
B(x, y) 215
Banach space 178
Basis 75 294
Basis, orthonormal 295
Bernstein polynomials 202
Bessel's inequality 270 299
Best approximation 150 194 268
Bijection 11
Binomial coefficient 51
Binomial theorem 51 201
Bolzano — Weierstrass property 162
Bolzano — Weierstrass theorem 23
Bolzano — Weierstrass theorem for sequences 40
Bounds, lower and upper 21 35
C 73
cardinal number 19
Cartesian product 7
Cauchy convergence criterion 41 45
Cauchy sequence 101 178
Cauchy — Schwarz inequality 88 96 256 257
Chebyshev norm 195
Chebyshev polynomials 198 266
Chebyshev polynomials of the second kind 267
Chebyshev theory 195
Closed disc 108
Closed set 28 107 156
Closure 157
Cluster point 22 35 159
Cluster point, greatest, least 25 36
Collection 29
Compactness 29 141
Compactness, countable 162
Compactness, relative 141
Comparison Test 48
Complement 7
Complete orthonormal set 295
Completeness 4 25 42 47 57 102 179
Complex number 5
Condition number 239
conjugate 5 80
Connectedness 169
Continuum Hypothesis 19
Contraction constant 116
Contraction mapping 116
Convergence in mean square 303
Convergence of a sequence 36 43 98 164 178
Convergence of a series 45 179
Convergence, absolute 46 179
Convergence, pointwise 60
Convergence, strong 308
Convergence, uniform 59
Convergence, weak 308
Countability 14
C[a, b] 59 73 93 177
De Morgan's laws 9
Definite integral 58 65
Derivative 57
Derived set 159
Determinant 82
Diameter 110
Differential equations 58 123 129
DIMENSION 75
Distance function 85
Distributive laws 235
Domain 10
Double integral 58
Dual space 219 282
Economisation of power series 206
Eigenvalue, eigenvector 225 286
Empty set 6 8
Equal-ripple property 197
Equicontinuity 145
Equivalent norms 189
Error 237
Euclidean space 87 252
Finite differences 153
Fixed point 116
Fixed point theorem 116 152
Fourier coefficients 299
Fourier series 58 298 299
Fourier series theorem 297 299
Fredholm integral equation 126 243
Functional 13 218
Functional analysis 3
Functions 10 52 see
Functions, bounded 55
Functions, complex-valued 58
Functions, composition of 13
Functions, constant 54
Functions, continuous 52 53
Functions, identity 14
Functions, inverse 13
Functions, one-to-one 11
Functions, onto 11
Functions, uniformly bounded 145
Functions, WEIGHT 265
Gram matrix 280
Gram — Schmidt orthonormalisation process 261
Graph 52 222
Greatest lower bound 21 35
Greatest-integer function 53
Hamel base 295
Harmonic series 46
Hausdorff space 160
Heine — Borel theorem 31
Heisenberg 282
Heisenberg's uncertainty principle 249
Hermite polynomials 267
hilbert 282
Hilbert space 281
Hoelder inequality 89
Homeomorphism 167
Image 11 164
Image, inverse 164
Imaginary part 5
Infimum 22
Injection 11
Inner product 252
Inner product space 252
INTEGER 4
Integral equations 2 137
Integral equations, Fredholm 126 243
Integral equations, nonlinear 133
Integral equations, Volterra 127 229
Interior 157
| Intersection 7
Intervals 20
Irrational number 4
Isomorphism 74 305
Jacobi polynomials 267
Kernel 220
Laguerre polynomials 267
Least squares approximation 195 267
Least upper bound 21 35
Least Upper Bound Axiom 26
Lebesgue integral 281
Legendre polynomials 264
LIMIT 36 98
Limit Comparison Test 51
Limit, greatest, least 26 36
Limit, inferior, superior 36
Limit, point 26 159
Lindeloef's theorem 171
linear combination 75
Linear dependence 75 260
Linear mapping 210
Linear space 70
Lipschitz condition 118
M 111
MAP 13
Mappings 13 113 see
Mappings, additive 236
Mappings, affine 228
Mappings, bounded 210
Mappings, closed 222
Mappings, continuous 115 164 165
Mappings, contraction 116
Mappings, homogeneous 236
Mappings, identity 114 213
Mappings, ill-conditioned 239
Mappings, inverse 225
Mappings, linear 210
Mappings, momentum 249
Mappings, perfectly conditioned 239
Mappings, perturbation 130
Mappings, position 249
Mappings, product of 113 231
Mappings, unitary 308
Matrix 79
Matrix, hermitian 287
Matrix, inverse 82 241
Matrix, symmetric 288
Maximum, minimum 21 35
Metric 85 176
Metric space 44 85
Metric space, closed 107
Metric space, complete 102
Metric topology 157
Metric, associated 177
Metric, chordal 92
Metric, discrete 94
Metric, Euclidean 87
Metric, homogeneous 185
Metric, induced 177
Metric, natural 86
Metric, sup 92
Metric, translation invariant 185
Metric, trivial 94
Metric, uniform 92
Minimax approximation 151 195
Minkowski inequality 89
Modulus 5
Moments 204
Neighbourhood 20 159
Nested intervals axiom 25 42 47
Newton's method 115
Norm 175 256
Norm of a functional 219
Norm of an operator 216
Norm, Chebyshev 195
Norm, cubic 185
Norm, matrix 242
Norm, octahedral 185
Normal equations 271
Normed space 176
Normed space, strictly convex 193 268
Null set 6
Null space 220
Numerical analysis 131 153 235
Observables 249
One-to-one correspondence 14
Open ball 158
Open base 170
Open covering 30 161
Open covering, countable 162
Open set 28 156
Operator 13 211
Operator, adjoint 285
Ordered pair 6
Orthonormal set 259
Orthonormal set, complete 295
Orthonormal set, total 299
Parallelogram law 257
Parseval's identities 299
Perturbation 130 237
Picard's theorem 123
Point set 20
Polarisation identity 278
Pre-Hilbert space 252
Preimage 164
Probability density function 204
Pythagorean identities 278
quantum mechanics 248 282
RANGE 11
Ratio Test 50
Rational number 4
Real number 4
Real part 5
Restriction 107
Riemann integral 58
Riemann — Lebesgue lemma 303
Riesz representation theorem 273 282
Riesz — Fischer theorem 305
Riesz — Frechet theorem 275
Root test 51
Rubber sheet geometry 168
S 97
scalar 69
Scalar, multiple 70
Scalar, product 251 252
Schroedinger 282
Second axiom of countability 170
Self-adjoint operator 285
Semimetric space 97
Seminorm 187
Separability 288
Separation 161 169
SEQUENCE 33
Sequence, Cauchy 101 178
Sequence, complex-valued 42
Sequence, convergent 36 43 98 164 178
Sequence, decreasing, increasing 38
Sequence, monotone 38
Sequence, uniformly convergent 60
Series 45
Series, absolutely convergent 46 179
Series, conditionally convergent 46
Series, geometric 49 229
Series, harmonic 46
Series, uniformly convergent 67
Sets 3
Sets, bounded 21 110
Sets, closed 28 107 156
Sets, compact 29 143 161 178
Sets, countable 15
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