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Korner T.W. — Fourier Analysis

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Название: Fourier Analysis

Автор: Korner T.W.

Аннотация:

Ranging from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering, the techniques and results of Fourier analysis and applications are displayed in perspective.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 591

Добавлена в каталог: 14.06.2009

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Предметный указатель

Labeyrie, diameters of stars      484—485
Lagrange, links with Fourier      170—171 476 478—479
Laplace doubts about Fourier's work      478—479
Laplace states central limit theorem      347
Laplace transform analyticity      379—382
Laplace transform analyticity (and analytic extension)      382—384
Laplace transform and stability      368 388—406
Laplace transform elementary properties      374—377
Laplace transform importance in number theory      546—551
Laplace transform in solution of linear differential equations      377—378
Laplace transform is analytic      379—382
Laplace transform need for care      386 4036
Laplace transform uniqueness      373—374 384—385
Laplace transform, connection with Fourier transform      372—373
Laplace transform, defined      372—373
Laplace transform, inversion (numerical)      386
Laplace transform,inversion      373—374 386—388
Laplace work on heat equation      274 478—479
Laplace's equation      see also “Dirichlet problem”
Laplace's equation connection with analytic functions      122—124 126—129
Laplace's equation connection with Brownian motion      55 451—453
Laplace's equation Gauss mean value theorem      129
Laplace's equation maximum principle      129—130 135—136
Law of errors      347 583;
Lebesgue mathematically infra dig      42—43
Lebesgue measure essential for later work      572
Lebesgue measure strikes panic into engineers      406
Lebesgue on generalisation      572
Lenstra, work on factorisation      512
Lerch's theorem, uniqueness of Laplace transform      384
Levy analytic maps of Brownian motion      458
Levy early interest in non differentiability      43
Levy interest in Brownian motion      45
Levy uniqueness of Brownian motion      583
Liapounov and central limit theorem      347
Liapounov method for proving stability      79—98
Linear programming, Fourier's interest in      480 499
Liouville and Kelvin      178 271
Liouville life      175—178
Littlewood long paper with Cartwright      114
Littlewood on Euler's formula      525
Logarithm of complex number elementary facts      535—536
Logarithm of complex number elementary problems      536
Logarithm of complex number elementary problems (resolved)      541—542
Long time averages      29—30 392
Lyell, Principles of Geology      282—283
Mathematical Brownian motion      see also “Brownian path”
Mathematical Brownian motion connection with analytic functions      454—460
Mathematical Brownian motion connection with Laplace's equation      55 451—453
Mathematical Brownian motion dimensional differences      451—454
Mathematical Brownian motion heuristic construction      50—55
Mathematical Brownian motion nowhere differentiable      55
Mathematical Brownian motion probability of return      451—454
Mathematical Brownian motion rigorous construction given by Wiener      45
Mathematical Brownian motion studied by Bachelier, Kolmogorov, Levy and Wiener      45 583—584
Mathematical Brownian motion, will it tangle?      461—466
Mathematicians      see also “Cambridge”
Mathematicians condescend to help scientific brother      290
Mathematicians good thing      43
Mathematicians, how recognised      178
Maximum methods for uniqueness, Dirichlet problem      134—135
Maximum methods for uniqueness, heat equation      344—346
Maxwell admires mirror galvanometer      334 575—576
Maxwell on stability      365—366
Maxwell relations with Kelvin      272—273 575
Mean square approximation      145—150 183
Mean square convergence      155—158 184
Measure theory, essential for later work      469 572
Meyer, wavelets      23
Michelson, interferometer      62 487
Mirror galvanometer      334 575—576
Moewus, amazing luck      427—428
Moment problem      21—23 385
Monte Carlo method      46
Monte Carlo method for integration      46—47
Monte Carlo method for Laplace's equation      47—49
Newton, and double tides      24
Non-linear differential equations general remarks      99 112 114—115
Non-linear differential equations stability      79—98
Non-linear differential equations, Duffing's equation      101—115
Nowhere differentiable functions and mathematical Brownian motion      51—55
Nowhere differentiable functions construction      38—41
Nowhere differentiable functions exist in real world      43—45
Numerical computation differential equations      115
Numerical computation Fast Fourier Transform      497—499
Numerical computation Fourier transform      481—490
Numerical computation integrals      46—47 191—196
Numerical computation tides      29—30
Numerical computation uniform approximation      215—217
Numerical computation, central to mathematics      558
Numerical computation, Dirichlet's problem      47—49
Numerical computation, easy to make mistakes in      436
Numerical computation, futile overelaboration      37
Numerical computation, Gibbs phenomenon      65—66
Numerical computation, inverse Laplace transform      368
Numerical computation, Parkinson's law for      497
Organs, electronic      35
Orthonormality of eigen functions      181
Orthonormality, defined      147
Orthonormality, for polynomials      185—190
Oxford breakaway technical college somewhere in the fens      see “Cambridge”
Oxford stories      481

Oxford, professorial appointments      505
Parseval's formula      156—157 184 187
Pathologies, not always as black as painted      23 45
Pearson, inventor of chi squared test      419
Peaucellier's linkage      198—200
Perrin description of Brownian motion      43 52—54
Perrin nature need not be smooth      43 98
Perrin says nice things about mathematicians      43
Picard's little theorem discussed      467
Picard's little theorem proof via Brownian motion      467—469
Poincare      42 347 582
Poisson annoys Jacobi      532
Poisson reality of eigen values      182
Polya's theorem, on return for random walks      443—449
Polynomials      see also “Tchebychev polynomials” “Trigonometric “Weierstrass
Polynomials, best uniform approximation by      202—217
Polynomials, Legendre      188—190 192—196
Polynomials, orthogonal      185—190
Principal character      533
Principle of the argument, proved      577—579
Principle of the argument, used      397—399
Random variables      see “Sums of independent random variables”
Random walk      443—450
Regression to mean      430
Resonance      95—98
Revest, secret codes      505 509
Riemann Lebesgue lemma      260—261 489 573—574
Rutherford, age of earth      290—291
Schonage, fast multiplication      502
Second order differential equations      see “Damped oscillator” “Sturm
Shamir, secret codes      505 509
Simple singularities, treatment of discontinuities and Fourier series      59—66
Simple singularities, treatment of discontinuities and Fourier transforms      300—307
Simple singularities, treatment of key idea      61
Simple singularities, treatment of poles and Laplace transforms      388—391
Stability for damped oscillator      79—97
Stability general remarks      97—98 365—367
Stability via Laplace transform      368 388—406
Stability, types of instability      365—366 368—369
Stars, diameter of      62 484—487 559
Stieltjes, convergence of Gaussian quadrature      195—196
Strassen, fast multiplication      502
Sturm Liouville theory, Fourier's investigation      170—174
Sturm Liouville theory, general      179—184
Sturm, “Voila mon affaire!”      211
Subsoil temperature      25—27
Summation methods      see “Sums”
Sums      see also “Fourier sums”
Sums of independent random variables      see also “Central limit theorem”
Sums of independent random variables and convolution      253
Sums of independent random variables, Cauchy      246—252
Sums of independent random variables, general      245—246
Sums of independent random variables, normal      246—250
Sums, Cesaro      4
Sums, de la Vallee Poussin      56—57
Sums, Fejer      4—10 56 407
Sums, general remarks      4 120
Sums, Poisson      116—120
Tait superiority of mathematical argument      290
Tait, Thomson and Tait      273
Taylor's theorem primitive version      352
Taylor's theorem, discussed      15—17
Tchebychev and uniform approximation      202—206 212—215
Tchebychev equiripple criterion      202—206 212 215
Tchebychev interest in mechanisms      197 201
Tchebychev polynomial and best uniform approximation      212—217
Tchebychev polynomial orthogonality      187
Tchebychev polynomial, defined      19—20
Tchebychev proves central limit theorem      347
Thomson      see “Kelvin Lord”
Time delay equation      395—402
Titchmarsh, and Hardy      481
Transatlantic cable      332—337
Transcendental numbers, Liouville's construction      176
Transients      91—92
Trigonometric polynomials, definition      10
Trigonometric polynomials, uniformly dense      10
Trigonometric polynomials, uniformly dense (result used)      12 19 97
Tukey, Fast Fourier Transform      499
Tychonov, non-unique solution of heat equation      338—343
Ulam, Monte Carlo method      46
Uniqueness of factorisation and Euler's formula      526
Uniqueness of factorisation and group of units modulo n      506—507
Vladivostok, telephone directory      591
Von Neumann on mathematics      v
Wallis, codebreaker and mathematician      505
Watt governor      365
Watt parallelogram      197 201
Watt redesigns steam engine      197
Wave equation      324—331
Wavelets      23
Weierstrass and existence of minima      126 208
Weierstrass nowhere differentiable function      38—41
Weierstrass polynomial approximation theorem, context      15—17
Weierstrass polynomial approximation theorem, proofs      17—18 19—20 292—294
Weierstrass polynomial approximation theorem, used      186 196
Weierstrass, proof of Weierstrass's theorem      292—294
Weyl's theorem, on equidistribution      11—13
Wiener, constructs Brownian motion      45
Wilbraham, Gibbs phenomenon      66 499
Zaremba, non existence of solution to Dirichlet's problem      140 163—164
Zeta function, brief appearance      551

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