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Vilenkin N.Y., Gel'fand I.M. — Generalized Functions. Volume 4. Applications of Harmonic Analysis
Vilenkin N.Y., Gel'fand I.M. — Generalized Functions. Volume 4. Applications of Harmonic Analysis

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Название: Generalized Functions. Volume 4. Applications of Harmonic Analysis

Авторы: Vilenkin N.Y., Gel'fand I.M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 398

Добавлена в каталог: 09.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $K{M_{p}}$      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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