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Kahane J.P., Bollobas B. (Ed) — Some Random Series of Functions
Kahane J.P., Bollobas B. (Ed) — Some Random Series of Functions

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Название: Some Random Series of Functions

Авторы: Kahane J.P., Bollobas B. (Ed)

Аннотация:

This second edition covers random series in Banach and Hilbert spaces, random Taylor or Fourier series, Brownian motion and other Gaussian processes, plus certain types of random sets and measures — subjects of application in mathematics, statistics, engineering and physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1993

Количество страниц: 3192

Добавлена в каталог: 05.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(n, d, \gamma)$ processes      263 289
$M_0$-set      250 288
$M_{\beta}$-set      250
$\beta$-quasi-helix      137
$\beta$S-helix      136
$\Lambda_{\alpha}$      88
$\Lambda_{\beta}(E,\mathbb{R}^n)$      139
$\varepsilon$-covering numbers      129 134
$\varepsilon$-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 $\mathbb{T}^q$      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 $(n, d, \gamma)$ 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, $\beta$-      136
Helices, $\beta$-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, $(n, \gamma)$      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
1 2
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