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Drmota M., Tichy R.F. — Sequences, Discrepancies and Applications
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Название: Sequences, Discrepancies and ApplicationsАвторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 503Добавлена в каталог: 19.05.2006Операции: Положить на полку |
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392 204 407 341 (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, 29 37 64 372 393 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, 316 Sequence, ( 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 ( 64 Sequence, uniformly distributed 2 204 Sequence, uniformly distributed mod ( 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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