Blei R. — Analysis in Integer and Fractional Dimensions :: Электронная библиотека попечительского совета мехмата МГУ

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Blei R. — Analysis in Integer and Fractional Dimensions

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Название: Analysis in Integer and Fractional Dimensions

Автор: Blei R.

Аннотация:

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on "dimension" as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Fréchet measures in stochastic analysis. This book is primarily aimed at graduate students specializing in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable as a textbook. It is also of interest to computer scientists, physicists, statisticians, biologists and economists.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2001

Количество страниц: 576

Добавлена в каталог: 22.05.2005

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Предметный указатель

Tail-probabilities, gauge (scale) of interdependence      297—299 320 363—364
Tail-probabilities, measuring independence      295 297—298
Tail-probabilities, polynomial estimates      364 524
Tensor norms (definitions) $||.||_{F_k}$ (instance of injective tensor norm)      60
Tensor norms (definitions) $||.||_{V_k}$ (instance of protective tensor norm)      82
Tensor norms (definitions) $||.||_{\check{\bigotimes}}$ (injective tensor norm)      82
Tensor norms (definitions) $||.||_{\tilde{\bigotimes}}$ (proactive tensor norm)      82
Tensor norms (definitions), g-norms      39 85—86
Tensor norms (definitions), greatest and least crossnorms      82
Tensor product (definitions) in dimension 3/2      Chapter XII $\S4$
Tensor product (definitions) in fractional dimension      467—469
Tensor product (definitions), algebraic      72—73 81
Tensor product (definitions), injective      82
Tensor product (definitions), projective      81
Tensor representations of restriction algebras      see also restriction algebras; tensor products; tensor norms
Tensor representations of restriction algebras in general setting      193—194
Tensor representations of restriction algebras,       161
Tensor representations of restriction algebras, $A(R^U)=V_U(\mathbb{N}^m)$       237
Tensor representations of restriction algebras, $A(R_n)=V_n|_{D_n}$       163
Tensor representations of restriction algebras,       161
Tensor representations of restriction algebras, $B(R^n)=\tilde{V}_n(R,...,R)      167
Tensor representations of restriction algebras, $B(R^U)=\tilde{V}_U(\mathbb{N}^m)$       237—238
Tensor representations of restriction algebras, $C_{R_n}=F_{n\sigma}$       163 167
Tilde algebra      79—80 see
Time homogeneity (assumption in Brownian movement)      282—283 330
Time-directions      445
Time-independence      350 394
Time-inhomogeneity      523
Time-sequence dependence      396 444—447
Transforms       141
Transforms of $F(\Omega)$ -measures      520
Transforms of $f\in L^1(\Omega,\mathbb{P})$       141
Transforms of -measure      264
Transforms of convolution of -measures      266
Transforms, Fourier      196 (Exercise 1)
Transforms, Fourier — Stieltjes      136
True F-measures      108 508 509 514 520
Truncation argument (in proof of Grothendieck's inequality)      49
Type       63 186 340—341
Type and       443—447 512—515 519
Type       78 186
Type, optimal $\mathfrack{D}$ -type      515

Type, optimal $\mathfrack{F}$ -type      514 530
Uniformizable $\Lambda(2)$ -set (definition)      210
Uniformizable $\Lambda(2)$ -space (definition)      46
Uniformly incident cover      470
Variation      see also Frechet variation; p-variation; Quadratic variation
Variation in sense of Prechet      2—3 126
Variation in sense of Vitali      2 127
Variation, total variation of measure      112
von-Neumann inequality      11
W-polynomials      141
Walsh characters      146
Walsh functions      146
Walsh series      see Series
Walsh system character group of $\Omega$       146
Walsh system of continuously increasing index      499—500
Walsh system of integer order      147—148
Walsh system of non-integer order (preview)      175
Walsh — Wiener series      see series
White noise, associated with -additive process      422 (Exercise 30 ii)
White noise, associated with a product of Wiener processes      405
White noise, associated with integrator      355 358 394
White noise, associated with p-stable motion      422 (Exercise 30 i)
White noise, associated with Wiener process      111 202—203
White noise, n-dimensional (question)      319
Wiener -measure: definition      110—111 292
Wiener -measure: generalized      293—294
Wiener -measure: variations      Chapter X $\S6$
Wiener Chaos      see also nth Wiener Chaos process
Wiener Chaos of order n      320
Wiener Chaos, decomposition      320
Wiener integral, definition      290
Wiener integral, generalization      358—359
Wiener measure      288
Wiener process, constructions      286—288
Wiener process, definition      285—286
Wiener process, generalized      293—294
Wiener process, least complex model      311
Wiener process, limit of simple random walks      283—284 329
Wiener process, preview      17—18 (Exercise 8)
Wiener process, series representation      294—295
Wiener process, Wiener's first approximation to Brownian movement      329
Wiener space      287—288

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