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Kahane J.P., Bollobas B. (Ed) — Some Random Series of Functions |
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Предметный указатель |
processes 263 289
-set 250 288
-set 250
-quasi-helix 137
S-helix 136
88
139
-covering numbers 129 134
-entropy 134
Adler 289
Almost periodic sequence (generalized) 72
Almost sure 2
Almost surely everywhere 9
Analytic continuation and summability 26—27
Analytic set 10 281
Anderson 283
Arnold 283
Assouad 137 139 286
Banach spaces, homogeneous, prehomogeneous 63—64
Banach spaces, Khintchin's inequalities 282
Banach spaces, random series in 11 -27
Banach spaces, type and cotype 282
Beppo — Levi theorem 6
Berman 289
Bernstein inequality 49
Beurling 287
Bienayme inequality 7
Billard xi 46 54 58 281 284 285 286
Blackwell 38
Borel 37
Borel field 3
Borel — Cantelli lemma 3 287
Borel — Cantelli lemma, generalized 172
Borell 282
Bounded series 12
Bourgain 78 79 284
Brillhart 75
Brownian fractional 263 267 289
Brownian functionals 288
Brownian helix 135 233
Brownian motion 125 233 288
Burkholder 282 288
Cantor triadic set 128 132 250
Capacity 128 132 204
Capacity, newtonian (and polar sets) 242
Carleson 286
Carlitz 75
Cartan 258
Cartan — Thullen theorems 38 45 283
Characteristic function 6
Circular set 189
Clunie 283
Concentration function 26
Conjugate harmonic functions 121
Contraction (principle of) 11 20 281
Convergence of a random Fourier series, almost everywhere 51 54
Convergence of a random Fourier series, uniform, everywhere 58
Convergence of a random series in probability 17
Convergence of a random series, almost sure 11 28
Convergence of a random series, essential 11 25
Convergence of a random series, necessary and sufficient conditions 28 33 34
Covering (random) 143
Covering (random) of a subset of 153
Covering (random) of the circle 144
Covering (random), uncovered sets 164
Csordas 284
Curves, Assouad 137 139
Curves, Peano 139 142
Curves, von Koch 129 137 138
Cuzick 285 289
Davis 288
de Leeuw 284
Dechamps 284
Dimension of cartesian products 140
Dimension of helices 136
Dimension of images, graphs, level sets 139 289
Dimension of intersections 141
Dimension of quasi-helices 137
Dimension, entropy 164
Dimension, Fourier 250
Dimension, Hausdorff 128 130
Dirichlet kernel 110
Dirichlet series 43 283
Dirichlet theorem 261
Distribution of a random variable 3
Divergence of a random Fourier or Taylor series, almost everywhere 53 116
Divergence of a random Fourier or Taylor series, everywhere 106 285
Domain of convergence, domain of holomorphy 41 45
Drury 284
Dubinsky 282
Dudley xi 129 211 212 218 219 225 230 238 288
Dudley integral 219
Dvoretzky 94 143 233 285
El Helou xiii 162 286
Energy integral 132 204
Entropy dimension 164
Equally distributed random variables 3
Equidistributed random variables 3
Erdoes 94 285
Event 1
Expectation 1 5
Fathi 288
Fejer sums 48
Fejer theorem 63
Fernique xi 129 176 211 212 221 223 225 230 287
Figa — Talamanca 285
Fourier coefficients xii 47 60
Fourier dimension 250
Fourier transforms 166
Fourier — Lebesgue divergent series 116
Fourier — Lebesgue series 47
Fourier — Stieltjes series 47 109
Fourier — Wiener series 235
Fournier 283
Fractals xiii
Fractional brownian motion, processes, images 263 267 289
Franklin — Wiener series 238
Frostman 128 129 130 132 133 286
Frostman Lemma 130 132
Fubini — Jessen theorem 6 281
Garling 282
Gatesoupe 288
Gaussian processes 263
Gaussian analytic functions 287
Gaussian Fourier series xi 197—210 226 285
Gaussian Hilbert space 211
Gaussian normal variable 67
Gaussian processes 211 212 288
Gaussian processes with stationary increments 212
Gaussian random variable 165 168
Gaussian series xi 165 173
Gaussian series in a Banach space 175
Gaussian Taylor series xi 178—196 287
Gaussian trigonometric series 197
Gauthier 283
German 289
Goldman 289
Graph dimension 139
Graph of a random function 278
H.a.p. sequences 72
Haagerup 282
Halasz 284
Halchin 284
Harmonic functions (conjugate) 119 121
Hartman 72
Hausdorff 128 286
Hausdorff measures and dimension 128 129 130
Hawkes 162 164 287
Helices 129 135
Helices, - 136
| Helices, -quasi 137
Helices, brownian 135
Helices, quasi- 129 137
Helson sets 72 284 288
Hilden 284
Hoffmann — Jorgensen 162 282 286
Holder condition 263 see
Homogeneous Banach space 63
Homogeneous chaos 125
Horowitz 289
Hruscev 288
Hunt 285
Image, brownian 250—261
Image, dimension 139
Image, fractional brownian 262—272
Independent increments 234
Independent random objects 5
Inequality, I (Bienayme) 7
Inequality, II (Paley-Zygmund) 8
Inequality, Khintchin type 18 282
Inequality, Kolmogorov 28 29 283
Inequality, Paley — Zygmund 28 30 31 50 96 103
Inequality, Paul Levy 15 281 283
Inequality, Pisier 23
Inequality, S.Bernstein 49
Inequality, Salem — Zygmund 67 285
Integrability (strong) of gaussian vectors 176
Integrability (strong) of Radernacher series 20 23
Ionesco Tulcea 284
Irregularity of random functions 93—108
Ivasev — Musatov 288 289
JAIN 282 285
Jakob 283
Janson 287
Kahane 284
Kakutani 233 288
Katznelson xii 218 284
Kaufman 263 272 284 287 288 289
Khintchin 282
Khintchin inequalities 282
Khintchin law of the iterated logarithm 233 238
Klein 289
Kolmogorov 2 28 29 109 121 129 134 281 282 283 286
Korner xii 288
Kronecker theorem 112
Kwapien 23 282
Lacunary trigonometric series 35 65 108 284
Lai Tze-leung 285
Level sets, dimension 139
Level sets, fractional brownian 272
Level sets, of gaussian Fourier series 204
Levy 15 233 263 281 283
Levy inequality 15 281 283
Levy processes 289
Linear mappings (norms and weak type) 66
Lipschitz conditions and classes 64 83 88 139 see
Littlewood 122 284
Local time 263
Loeve 2
Malliavin 198 209 284
Mandelbrot xiii 162 263 286 289
Mantero 285
Marcinkiewicz 281
Marcus xi xii 211 213 215 226 282 284 285 288 289
Marcus — Pisier theorem 213 226—231
Marcus — Shepp comparison principle 213 215
Maurey 282
Meyer 2
Modulus of continuity 86
Moments 6
Murai 283
Mutafian 36
Nevanlinna theorem 121
Nisio 285
Non-flattening convex sets 158
Non-gaussian Fourier series 226
Nordlander 282 283
Normal sequences 168
Normal variables 67 168
Nowhere differentiable functions 105 108 129
Occupation density 263 267
Offord 283
Orey 233 286 288 289
Paley xi xii 8 38 94 109 282 283 284 285
Paley — Zygmund inequalities 28 30 31 50 96 103
Paley — Zygmund theorem 46 53 54
Parseval formulas 167
Peano curve 139 142
Pelczynski 282
Perkins 288
Peyriere 36
Pisier xi xii 23 211 213 215 218 226 282 284 285
Pisier algebra xii 211 213 215
Pitcher 284
Pitt 289
Poisson kernel (and conjugate) 118 122
Poisson sums 48
Poisson transforms (and conjugate) 118 122
Polar sets 242
Pollard 287
Polya 133
Polynomials with unimodular coefficients 75
Pommerenke 283
Principle of contraction 11 20
Principle of reduction 9
probability 1 2
Probability space 1 2
Probability space, standard, product 4
Processes, 263
Processes, gaussian 211 212 288
Processes, Levy 289
Processes, stationary 199
Processes, Wiener 233 234
Processes, with stationary increments 212
Quasi-helices 129
Queffelec 283 284
R.a.p sequences 72
Rademacher 282
Rademacher and gaussian Fourier series 226
Rademacher and Steinhaus series 22
Rademacher Fourier series 46 49—53 58 285
Rademacher functions 1
Rademacher sequences 2 5
Rademacher series xi 11 18 32 282
Random covering 143—164
Random Dirichlet series 43 283
Random element 2
Random Fourier series, trigonometric series 46—66 83—108 197—211 226 285
Random function 9
Random object 2
Random point masses 109—127
Random series in a Banach space 11—27 282
Random series in a Hilbert space 28—36 283
Random series, positive 32
Random Taylor series 37—45 178—196 283 287
Random translates 143—164
Random trigonometric polynomials (bounds, simultaneous inequalities) 67 69 103
Random variable 1 3
Random vectors 11 28
Range of a gaussian Fourier series 200
Range of a gaussian Taylor series 180
Rapid points of brownian motion 239 242 288
Recurrence 165 173 287
Reduction principle 9
Regularity of random functions 83—91
Rider 284
Riesz (F.) products 112
Riesz (M.) theorem 121
Rosenthal 282
Rudin 75
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