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Drmota M., Tichy R.F. — Sequences, Discrepancies and Applications
Drmota M., Tichy R.F. — Sequences, Discrepancies and Applications

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Название: Sequences, Discrepancies and Applications

Авторы: Drmota M., Tichy R.F.

Аннотация:

The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 503

Добавлена в каталог: 19.05.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-complexity      392
$\mu$-continuity set      204
$\varepsilon$-approximation      407
$\varepsilon$-net      341
(t,m,s)-net      382
(t,s)-sequence      382
Abel summation      98 127 264
Abel's summation method      268 273
Additive semigroup      363
Algorithm      374 377
Almost periodic      102
Analytic set      335
Approximation of functions      377
Approximation type      92
Arclength      288
Average case analysis      390
Badly approximate      67
Banach's fixed point theorem      387
Benford's law      276
Bernoulli polynomial      18 131
Bernoulli shift      324
Best approximation denominator      67
Binomial series      245
Boltzmann equation      414
Borel measure      204 313
Borel set      335
Borel — Cantelli lemma      161 187 197 267 331
Brownian motion      300 312
CAP      231 294
Cellular automaton      430
Central limit theorem      96
Cesaro mean      268
Chapman — Kolmogorov equation      310
Characteristic function      1
Characteristic polynomial      346
Chebyshev quadrature      399
Circle problem      27
Coanalytic set      335
Coloring      340
Continued fraction expansion      48
Continued fraction expansion, metric results      64
Continuously uniformly distributed      277
Continuously well distributed      277
Convex function      279
Convex set      9 213
Convolution      30 317
Correlation polynomial      326
Courant — Friedrichs — Levy condition      411
Covariance kernel      391
Cryptology      424 432
Curvature      213 407
Dedekind domain      346
Determinant of a lattice      67
Diaphony      24
Differential equation      237 403 410 414 419
Digital expansions      105
Dirac measure      30
Dirichlet's approximation theorem      68
Discrepancy      4 12 13
Discrepancy function      13 79 131
Discrepancy system      205
Discrepancy, $L^{2}$-discrepancy      29 37 64 372 393
Discrepancy, $L^{p}$-discrepancy      5 6 40 209 212 378
Discrepancy, Abel      268
Discrepancy, continuous      278
Discrepancy, cube      29 35 37
Discrepancy, Green function      14 421
Discrepancy, isotropic      9 13 71 248
Discrepancy, logarithmic      252
Discrepancy, lower bounds      29 40 41 44 47 213 231 241
Discrepancy, star discrepancy      5 6 49
Discrepancy, uniform      259
Discrepancy, upper bounds      71 213 232 241
Discriminant      142 244
dispersion      11 12 14 406
Dispersion, cap      406
Dispersion, slice      406
Distribution function      46 138 151
Eigenfunction      302
Empty spectrum      101
Entire function      16 282
Entropy method      199
Ergodic theorem      199 324
Ergodic transformation      199
Euler's summation formula      256 264
Exponential map      303
Exponential sums      14 127
Fejer kernel      18 79
Fibonacci numbers      293
Fourier coefficient      25 65 419
Fourier series      57 256 370
Fourier transform      17 30 234
Fractional part      1
Functional      2
Fundamental region      73
Gegenbauer polynomial      236
Generating function      326
Generator, discrete exponential      429
Generator, inversive congruential      429
Generator, multiplicative congruential      426
Generator, power      428
Generator, quadratic      428
Generator, random number      424
Geodesic ball      301
Geodesic distance      211 231
Good lattice point      369
Group, amenable      317
Group, compact      314
Group, locally compact      314
Group, reflexive      317
Group, representation      315
Haar measure      214 314
Harmonic polynomial      234
Hausdorff dimension      28 211
Hausdorff distance      407
Hausdorff measure      211
Heat equation      410
Helly's selection principle      139
Hilbert — Schmidt norm      234
Hyperplane      73 213 223
Inequality, Carlson — Hunt      160
Inequality, Cauchy      283
Inequality, Cauchy — Schwarz      23 167
Inequality, Chebyshev      324
Inequality, Erdoes — Turan — Koksma      15
Inequality, Erdoes — Turan — Koksma, Abel      272
Inequality, Erdoes — Turan — Koksma, continuous      279
Inequality, Erdoes — Turan — Koksma, limitation method      252
Inequality, Erdoes — Turan — Koksma, logarithmic      253
Inequality, Koksma — Hlawka      10
Inequality, Koksma — Hlawka, Abel      271
Inequality, Koksma — Hlawka, continuous      279
Inequality, Koksma — Hlawka, dispersion      14
Inequality, Koksma — Hlawka, limitation method      251
Inequality, LeVeque      23 24
Inequality, Minkowski      161
Inequality, Vaaler      15
Inequality, Van der Corput      289
Inequality, Weyl      105
Initial value problem      300
interval      1
Interval, k-dimensional      1
Irregularities of distribution      47
Iterated logarithm      162 198 301
Jacobi determinant      303
Jacobi equation      303
Jacobi polynomial      402
Karamata's method      275
Khintchine's theorem      63 64 78
Klosterman sums      29
Kolmogorov complexity      425
Kolmogorov's 0-1-law      325
Kronecker symbol      163
Kronecker's approximation theorem      15
Laplace — Beltrami operator      300 422
Lattice      67
Laurent series      385
Lebesgue measure      1
Legendre function, associated      236
Liouville number      252
Lipschitz condition      6 149 208
Littlewood conjecture      132
Lorentz condition      260
Low discrepancy sequence      369
Maldistribution      140
Markov process      301
Markov times      311
Marriage theorem      318
Matrix limitation method      250
Matrix method      430
Minkowski's theorem, linear forms      69
Minkowski's theorem, successive minima      77 78
Mixing condition      197
Modulus of continuity      12 14 378
Muentz polynomial      189
Newton polygon      284
Norm of an ideal      346
Normal number      104
Numerical integration      368
Ostrowski expansion      48
Parallel region      75
Pigeonhole Principle      68 76
Poisson's summation formula      18 79
Polar coordinates      298
Polytope      213
Q-additive function      91
q-additive function, strongly      91
q-multiplicative function, strongly      104
Quasi-Monte Carlo method      370 380 411
r-box      45
Rademacher function      29 45 224
Random variable      96 197 218 336
Random variable, weakly dependent      197
RANGE      14
Reduction modulu      1
Riemann integrable function      3
Riemann — Lebesgue lemma      18 371
Riemann's zeta function      26
Riemannian manifold      300
Risk-model      387
Rolle's theorem      191
Roth's theorem      29 40 223 394
S-unit equation      188
Schmidt's theorem      41 44 53
Sequence, $L^{1}$(G)-uniformly distributed      316
Sequence, ($n\alpha$)      48
Sequence, A-uniformly distributed      251
Sequence, completely uniformly distributed      118
Sequence, digital      91
Sequence, eutaxic      133
Sequence, exponential      118
Sequence, Faure      385
Sequence, feedback shift register      430
Sequence, Halton      41 369 380
Sequence, Hammersley      41 369 411
Sequence, Hartman uniformly distributed      315
Sequence, k(N)-distributed      190 324
Sequence, Kronecker      66
Sequence, lacunary      161
Sequence, linear recurring      143 346
Sequence, maldistributed      140
Sequence, random      188
Sequence, random number      424
Sequence, recurrent      142
Sequence, Rubel uniformly distributed      315
Sequence, shift register      431
Sequence, Sobol      386
Sequence, symmetrisized ($n\alpha$)      64
Sequence, uniformly distributed      2 204
Sequence, uniformly distributed mod ($R_{n}$)      151
Sequence, unitary uniformly distributed      316
Sequence, Van der Corput      41 368
Sequence, weakly uniformly distributed      356
Sequence, well distributed      2 96 259 262
Shatter function      341
Sierpinski gasket      210
Signed measure      241
Simultaneous approximation, denominator      67
Singularity      380
Slice      212 294
Space, arcwisely connected      291
Space, compact      313
Space, homogeneous      233 310
Space, k-dimensional Euclidean      1
Space, locally compact      314
Space, Polish      335
Spectral measure      200 201 265
Spectrum of a sequence      101
Sphere      220
Spherical design      399
Spherical harmonics      236
Squarefree integers      104
Star discrepancy      5 6 49
Stone — Weierstrass' approximation theorem      205
Subdivision      151
Successive minima      67
Summation method      249
Support function      220
Tarski's problem      27
Taylor coefficient      282
test      425
Test, serial      426
Test, uniformity      426
Thue — Siegel — Roth's theorem      92
Toeplitz's theorem      250
Topological dynamics      131 363
Topological semigroups      363
Torus      1
Trigonometric polynomial      18 20
Turing machine      424
Ultraspherical polynomial      403
Unimodal      96
Univeral bad      199
Universal good      199
Urysohn function      205
Van der Corput difference theorem      280
Van der Corput set      200
Vapnik — Chervonenkis dimension      341
Variation      10 16
Variation, bounded      20 162 371
Variation, Hardy and Krause      10 11
Variation, Vitali      10
Vinogradov's method      28
von Neumann kernel      315
von Neumann selection theorem      335
Weak measure      411
Weighted mean      250
Well distribution      259
Weyl's criterion      15
Weyl's criterion, continuous      278
Weyl's criterion, distribution functions      139
Weyl's criterion, limitation methods      251
Weyl's criterion, weighted      263
Wiener measure      304 391
Wiener — Schoenberg theorem      139
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