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| Авторизация |
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| Berg C., Christensen J.P., Ressel P. — Harmonic Analysis On Semigroups |
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| Предметный указатель |
 -bounded 90
 -positive, function 123 127
-positive, linear functional 124
-smooth measure 21 250 2
*-additive function 101
*-homomorphism of *-semigroups 87
*-semigroup 86
*-subsemigroup 87
2-divisible semigroup 98 113 133 224 231 251
Abelian semigroup 86 92
Abelian semigroup with involution 86 92
Absolute, polar set 13
Absolute, value on a semigroup 89
Absolutely, convex subset 2
Absolutely, decreasing function 140
Absolutely, monotone function 140
Absorbing, element 87 100 107
Absorbing, subset 2
Adapted, cone 42
Adapted, space 42 52 181
Admissible subset 123
Alaoglu — Bourbaki’s theorem 14 64
Algebraic dual space 10
Almost positive kernel 66
Alternating of infinite order 130
Analytic space 64
Appert — Varadarajan space 33
Approximation Lemma 145
Balanced subset 2
Barycentre 56
Base of a convex cone 59 88
Bauer simplex 59 95 96 131 158 169
Bernoulli, distribution 235
Bernoulli, random variable 226 229
Bernstein function 114 141
Bernstein’s Theorem 135
Bickel and van Zwet’s theorem 226
Bimeasure 24 33 64 206
Binomial distribution 165
Bipolar theorem 12
Birkhoff’s theorem 60
Bivariate generating function 165
Bochner’s theorem 96 157
Borel, measure 17
Borel, subset 17
Boundary measure 58
Bounded with respect to an absolute value 90
Bretagnolle, Dacunha-Castelle and Krivine’s theorem 149 176
BV-functions 143
Canonical topology of a finite dimensional space 13
Capacity 139 267
Centre of gravity 55 56
Chain majorization 251
Choquet theory 65
Choquet-Bishop-de Leeuw’s theorem 59
Classical Levy-Khinchin formula 216 221
Completely alternating, capacity 139
Completely alternating, function 130 263
Completely monotone in the classical sense 136
Completely monotone, capacity 267
Completely monotone, function 130 263
Completely negative definite function 229
Completely positive definite function 193 229
Complex moment 117
Complex moment, function 117
Complex moment, problem 117 193
Conditionally positive definite kernel 66
Cone 13
Continuity theorem for generating functions 162
Continuity theorem for Laplace transforms 123
Continuous on the right 136
Convex, combination 55
Convex, polyhedron 55
Convolution of finite Radon measures 29
Convolution, semigroup 100
Determinate, measure 180
Determinate, moment function 180
Determinate, positive definite sequence 200
Dirac measure 22
Doubly stochastic matrix 60 240 251
Douglas’ theorem 61
Dual, map (homomorphism) 97 207
Dual, pair 11
Dual, semigroup 93
Dvoretzky’s theorem 152 176
Dynkin class 28
Einhorn’s theorem 153 154
Elementary, doubly stochastic matrix 250
Elementary, random variable 227
Entropy function 218 240
Euler’s constant 140
Exponential of  50
Exponentially bounded, function 90
Exponentially bounded, positive definite function 90 92
Exponentially convex function 225
Extension, theorem for Radon contents 18
Extension, version of Hahn — Banach’s theorem 8
Extreme, boundary 55
Extreme, point 55
Extreme, ray 83
Extreme, subset 55
F-moment, problem 186
F-moment, sequence 186
Faraut and Harzallah’s theorem 174 177
Finest locally convex topology 4
Finite signed measure 39
Fubini’s Theorem 26
Function of positive type 88
Function, bounded with respect to an absolute value 90
Functions operating on positive definite, matrices 157
Gaussian semigroup 218
Generalized Laplace, transform 96 203
Generalized Laplace, transformation 96 203
Generating function 156 161 165
Generator set 127
Geometric version of Hahn-Banach’s theorem 6
Hahn — Banach theorems 5
Hamburger’s moment problem 186
Hamburger’s theorem 186
Hankel matrix 122
Hausdorff topological semigroup 29
Hausdorff’s moment problem 134 187
Haviland’s moment problem 187
Helly’s selection theorem 64
Hereditary on the left 119
Hermitian, function on a semigroup with involution 88
Hermitian, kernel 67
Hermitian, matrix 66
Hilbert matrix 122
Hilbert space representation of negative definite kernels 82
Hilbert space representation of positive definite kernels 81 82
Hildebrandt-Schoenberg’s theorem 134
Hoeffding’s inequality and degree r 232
Hoeffding’s inequality of all orders 230
Hoeffding’s inequality of order n 228
Homomorphism of semigroups 87
Hyperplane 5
Idempotent commutative semigroup 119
Identical involution 87
Image measure 28
Indeterminate, measure 180
Indeterminate, moment function 180
Indeterminate, positive definite kernel 76
Indeterminate, positive definite sequence 200
Indeterminate, probability measure on  163 164
Indeterminate, two-sided moment sequence 201
Inner measure 18
| Integral representation of bounded, Positive definite functions 96
Integral representations, theory of 55
Integrate superieure essentielle 62
Involution 86 123
Isomorphism of semigroups 87
Jordan — Hahn decomposition 39
Kisynski’s theorem 18 63
Krein — Milman’s theorem 57 65
Laplace transform 75 114 115
Levy — Khinchin formula 108 141
Levy, continuity theorem 97
Levy, function 108
Levy, measure 104
Localization principle 30
Locally, convex topological vector space 2
Locally, finite Radon measure 17 33 61 63
Log-normal distribution 201
Lower semicontinuous 20
Mackey topology 12 15
Mackey — Arens’theorem 15
Majorization 240 241
Marginal distribution 50
Maximal elements in a semigroup 252
Mean empirical variance 239 249
Mesure exterieure 62
Method of moments 185
Molecular measure 22 49 55 227
moment 116
Moment, function 116 179 222
Moment, generating function 222
Monotone of infinite order 130
Monotone, convergence theorem for Radon measures 20
Multi-dimensional moment problem 190
Multivariate majorization 241
Myope topology 268
Negative definite, function 89 253
Negative definite, kernel 67
Negative definite, matrix 66
Negative definiteness in the group sense 88
Negative definiteness in the semigroup sense 88
Negative definiteness of degree r 232
Neumann’s result 59 60
Nevanlinna, extremal measure 200
Nevanlinna, parametrization 200
Nonmetrizable first countable compact, dependent positive definite function 151
Nonmetrizable first countable compact, norm 3
Nonmetrizable first countable compact, space 121
Normal distribution 190
One-dimensional moment problem 185
One-point measure 22
One-sided stable measure of index a 217
Ordering of an idempotent semigroup 119
Parallelogram law 153
Perfect semigroup 203
Perfect semigroup, without zero 263
Poisson distribution 164 165 235
Polar subset 12
Polish space 16
Pollard — Tops^e’s theorem 35 36
Portmanteau theorem 45 46
Positive definite function 253
Positive definite, function 87 253
Positive definite, kernel 67
Positive definite, matrix 66
Positive definiteness in the group sense 88
Positive definiteness in the semigroup sense 88
Positive type 88
Potential kernel 142
Product, measure 26
Product, semigroup 87 97 204
Proper mapping 29
Pseudo-concentrated 58
Purely imaginary homomorphism 101
Quadratic form 101 234 246
Quasibounded 253
Quasibounded, below 253
Radon which is not locally finite 33
Radon, bimeasure 24
Radon, content 17
Radon, measure 17
Radon, real infinite dimensional hyperbolic space 173
Relatively compact subset of  51 52
Representation of a semigroup S 90
Representing measures, set of 52 180 181
Reproducing kernel Hilbert space (RKHS) 81
Restricted dual semigroup 96
Restriction of a Radon measure 21 53
Resultant 56
Reverse Hoeffding inequality 235
Riesz representation theorem 39 64
Schoenberg triple 148
Schoenberg’s theorem 74 85
Schoenberg’s theorem for the complex Hilbert sphere 171
Schoenberg’s theorem for the real Hilbert sphere 159
Schur of order n 242
Schur, concave function 240 241
Schur, convex function 240 241
Schur, decreasing function (of order n) 243
Schur, increasing function 243
Schur’s Theorem 69
Semicharacter 92
Semicharacter on an idempotent semigroup 119
Semigroup 86
Semigroup with involution 86
Seminorm 3
Seminorm, determined by a subset 3
Separation version of Hahn-Banach’s theorem 7
SEQUENCE 187
Shift operator 91 123
Signed, measure 17
Signed, Radon measure 39
simplex 59
Slutsky’s theorem 64
Sorgenfrey topology 31
Stable measure of index 218 219
Standard p-function 142
Stieltjes function 142
Stieltjes moment, function 193
Stieltjes moment, problem 187
Stieltjes’ theorem 187
Stochastic matrix 60
Strictly, kernel 67
Strictly, negative definite kernel 67
Strictly, positive definite function 87
Strong Hamburger moment problem 198
Sublinear function 8
Subsemigroup 87
Support of a function 39
Support of a Radon measure 22 32
Symmetric kernel 68
Tensor product of positive definite, kernels 70
Topological, dual space 10
Topological, group 1
Topological, semigroup 29 87
Topological, vector space 1
Topology, compatible with a duality 11
Topology, induced by a family of seminorms 4
Total variation norm 40
Two-sided moment, problem 198
Two-sided moment, sequence 198
Two-sided Stieltjes moment sequence 202
Vague, convergence of Radon measures 50
Vague, topology 50
Weak, convergence of finite Radon measures 45
Weak, topology on  45
Weak, topology,  11
Wells and William’s theorem 153
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