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| Авторизация |
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| Vilenkin N.Y., Gel'fand I.M. — Generalized Functions. Volume 4. Applications of Harmonic Analysis |
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| Предметный указатель |
Algebra of polynomials of two variables 232
Algebra with an involution 229
Algebra, normed 229
Algebra, topological 229
Annihilator 304
Annihilator, orthogonal complement of 327
Barreled space 6
Barrier sequence 161
Basis, biorthogonal 43
Basis, unconditional 42
Bernstein’s inequality 218
Bochner — Schwartz theorem 157
Bochner’s theorem 155
Commutation relations 362
Compactness 318
Compactness weak, in Hilbert space 318
Condition (N) 82 85
Convergence in Hilbert space (strong and weak) 27
Convergence type of sequence 98
Convergence weak, in countably normed space 73
Convolution 23 140
Convolution of functions from Z 166
Correlation functional with homogeneous and isotropic sthorder increments 297
Correlation functional with independent values 287
Correlation functional with stationary Kth-order increments 266 267
Correlation functional, Gaussian process 249
Correlation functional, homogeneous and isotropic 294
Correlation functional, random field homogeneous 290
Correlation functional, random process 247
Correlation functional, stationary process 264
Correlation functional, unit process 260
Correlation functional, Wiener process 259
Correlation matrix with homogeneous sth-order increments 300 301
Correlation matrix, isotropic multidimensional 301
Correlation matrix, multidimensional 298
Correlation matrix, random field homogeneous multidimensional 300
Correlation matrix, vectorial multidimensional 302
Cyclic, operator 121 123 129
Cyclic, subspace 130
Cyclic, vector 129
Direct integral of Hilbert spaces 114
Eigenspace 120
Eigenvector, generalized 105 119
Ellipsoid in Hilbert space 327
Equality of random variables 238
Exponent of convergence 88
Exponent of ellipsoid 89
Factor space 72
Fatou’s Lemma 145
Fourier transform of a measure 139
Function of random variables 239 240
Function of the second kind 213
Function, evenly positive definite continuous 211 226
Function, order of growth 87
Function, positive test 136
Function, positive-definite continuous 138 140 152
Function, rapidly decreasing 11
Function, symmetric relative to group 213
Functional dimension of linear topological space 98
Functional dimension of space U 102
Functional of random process with independent values 273
Functional on nuclear space 74
Functional on space K 18 19
Functional on space K(a) 17 18
Functional on space S 19
Functional, bilinear 2
Functional, characteristic 260
Functional, continuous in each argument 8
Functional, convex 3
Functional, correlation (see Correlation functional)
Functional, Hermitian bilinear 2 167
Functional, local 275
Functional, lower semicontinuous 4
Functional, multiplicatively positive on topological algebra 230
Functional, positive definite on linear topological space 347
Functional, translation invariant 167 169
Gaussian improper 251
Gaussian measure 335
Gaussian measure, degenerate (improper) 337
Gaussian process with independent values 288 289
Gaussian process, correlation functional of 249
Gaussian process, derivative of 257
Gaussian process, examples 257
Gaussian process, improper 251
Gaussian process, proper 248
Gaussian proper 248
Gaussian proper in the wide sense 268
Gaussian proper of generalized type 285 286
Gaussian proper with independent values 273
Gaussian proper with stationary nth-order increments 265
Gaussian proper, characteristic functional of 273 278
Gaussian proper, correlation functional of 264
Gaussian proper, derivatives of 257
Gaussian proper, examples 257
Gaussian proper, linear operations on 245
Gaussian proper, mean value of 263
Gaussian proper, nth-order moments 287 288
Gaussian proper, nth-order moments of 247
Gaussian proper, Poisson 282
Gaussian proper, spectral measure of 264
Gaussian proper, stationary 262 263
Generalized eigenvector 105 119
Generalized function on space  148
Generalized function, conditionally positive 176
Generalized function, conditionally positive definite 175
Generalized function, even 196
Generalized function, evenly positive definite 196
Generalized function, positive 136 142
Generalized function, positive definite 140
Generalized function, positive on space Z of one variable 220
Generalized function, positive on space Z of several variables 225
Generalized function, relative to group 214
Generalized function, symmetric relative to group 213
Generalized random field 243 289
Generalized random field and isotropic 292
Generalized random field with homogeneous and isotropic sth-order increments 294
Generalized random field, homogeneous 290
| Generalized random field, spectral measure of 293
Generalized random process 243
Generalized random process, derivative of 246
Half-space 303
Hilbert’s example 233
Kernel theorem for polylinear functional 20
Kernel theorem for space K 18
Kernel theorem, abstract 74
Kernel theorem, second formulation of 76
Krein’s theorem 196 197
Linear topological space, e-set in 86 87
Linear topological space, functional dimension of 98
Local functional 275
Measure in adjoint space of countably Hilbert space 318
Measure in Hilbert space 334
Measure of generalized random field 290
Measure of generalized random process 264
Measure of unit random process 264
Measure on compatibility condition for 309
Measure on conditions for 315
Measure on continuous 309 310
Measure on countably additive 372
Measure on cylinder sets (cylinder set measure) 307
Measure symmetric relative to group 214
Measure, CT-finite 350
Measure, degenerate (improper) 337
Measure, finitely additive 312
Measure, Fourier transform of 346
Measure, Gaussian 335
Measure, induced 311
Measure, quasi-invariant 352 355
Measure, random 268
Measure, regular 308 314
Measure, spectral 128
Measure, tempered 140
Measure, weak convergence of 349
Measures, equivalence of 351
Minimal order of growth, a function of 88
Moments with independent values 287 288
Moments, nth order of generalized random process 247
Muitiplicatively on space K 150
Muitiplicatively on space Q 201
Muitiplicatively on space S 150
Muitiplicatively positive generalized function 149 150
Multiplicative positivity 142
Multiplicatively positive functional 230
Norm, Hilbert — Schmidt 35
Norm, trace 49
Nuclear Lie group 362
Nuclear space (see Space)
Nuclearity criterion for countably Hilbert space 70
Nuclearity criterion for perfect countably Hilbert space 93 94
Operator in Banach space 55 56
Operator in nuclear space 124
Operator of Hilbert — Schmidt type 32
Operator with finite trace 38
Operator, completely continuous 28
Operator, cyclic 123 129
Operator, degenerate 26
Operator, nuclear 37
Operator, self-adjoint 123
Operator, strictly positive definite 26
Order of growth of function 87
Polar of a set 312
Radon — Nikodym theorem 351
Random field, generalized (see Generalized random field)
Random function 241
Random functional 242
Random measure 268
Random process 241
Random process, generalized (see Generalized random)
Random variable 237
Random variable, characteristic function of 241
Random variable, infinitely divisible 283
Random variable, mean value of 240
Realization of Hilbert space 110
Resolution of unity 127
Riesz’s theorem 137
Rigged Hilbert space 107
Schur’s Theorem 277
Series of functionals, absolutely convergent 67
Series of functionals, unconditionally convergent 67
Set bounded in countably Hilbert space or adjoint 60 61
Set bounded of eigenvectors, complete 120
Set bounded of random variables 238
Set bounded, base of 305
Set bounded, cylinder 303
Set bounded, generating subspace of 305
Set bounded, metric order, relative to neighborhood of zero 88
Set, absolutely convex 3
Set, absorbing 4
Space, adjoint to 59
Space, barreled 6
Space, countably Hilbert 62
Space, countably normed 63
Space, examples of 79
Space, linear topological 66
Space, locally convex linear topological 6 114 305
Space, nuclear 62 63
Space, perfect 72
Spectral decomposition 120
Spectral decomposition, theorem on 128
Symmetric homomorphism 230
Topology in countably Hilbert space and adjoints 60 61
Topology, defined by positive definite operators 333
Union space of linear topological spaces 330
Unit random field 245
Unit random process 244 260
Unit random process, correlation functional of 260
Unit random process, spectral measure of 264
Unitary operator in Hilbert space 121
Unitary operator in rigged Hilbert space 121
Unitary operator, cyclic 121
Unitary representation 363
Wiener process 245 258
Wiener process, correlation functional of 259
Wiener process, derivative of 260
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