دانلود کتاب Hilbert transforms:

عنوان فارسی :

دانلود کتاب هیلبرت تغییر شکل می دهد:

عنوان انگلیسی :

Hilbert transforms:

زبان : English

موضوع : Mathematics->Optimization. Operations Research

نویسندگان : Frederick W. King

ناشر : CUP

ISBN (شابک) : 9780521887625, 0521887623

تعداد صفحات : 898\898

سال نشر : 2009     ویرایش :

حجم : 3 MB       فرمت : pdf

قیمت : 20000 تومان

فهرست :



Table of contents :
Contents......Page 8
Preface......Page 22
Symbols......Page 26
1.2 Definition of the Hilbert transform......Page 41
1.3 The Hilbert transform as an operator......Page 44
1.4 Diversity of applications of the Hilbert transform......Page 46
Notes......Page 48
Exercises......Page 49
and......Page 51
2.3 Lipschitz and Hölder conditions......Page 52
2.4 Cauchy principal value......Page 53
2.5 Fourier series......Page 54
2.6 Fourier transforms......Page 59
2.7 The Fourier integral......Page 62
2.8 Some basic results from complex variable theory......Page 63
2.9 Conformal mapping......Page 77
2.10 Some functional analysis basics......Page 79
2.11 Lebesgue measure and integration......Page 85
2.12 Theorems due to Fubini and Tonelli......Page 95
2.13 The Hardy–Poincaré–Bertrand formula......Page 97
2.14 Riemann–Lebesgue lemma......Page 101
2.15 Some elements of the theory of distributions......Page 103
2.16 Summation of series: convergence accelerator techniques......Page 110
Notes......Page 117
Exercises......Page 120
3.1 Hilbert transforms – basic forms......Page 123
3.2 The Poisson integral for the half plane......Page 125
3.3 The Poisson integral for the disc......Page 129
3.4 Hilbert transform on the real line......Page 134
3.5 Transformation to other limits......Page 144
3.6 Cauchy integrals......Page 147
3.7 The Plemelj formulas......Page 151
3.8 Inversion formula for a Cauchy integral......Page 152
3.9 Hilbert transform on the circle......Page 154
3.10 Alternative approach to the Hilbert transform on the circle......Page 155
3.11 Hardy’s approach......Page 158
3.12 Fourier integral approach to the Hilbert transform on......Page 162
3.13 Fourier series approach......Page 169
3.14 The Hilbert transform for periodic functions......Page 172
3.15 Cancellation behavior for the Hilbert transform......Page 175
Notes......Page 181
Exercises......Page 182
4.1 Introduction......Page 185
4.2 Hilbert transforms of even or odd functions......Page 186
4.3 Skew-symmetric character of Hilbert transform pairs......Page 187
4.4 Inversion property......Page 188
4.5 Scale changes......Page 190
4.6 Translation, dilation, and reflection operators......Page 195
4.7 The Hilbert transform of the product......Page 200
4.8 The Hilbert transform of derivatives......Page 204
4.9 Convolution property......Page 207
4.10 Titchmarsh formulas of the Parseval type......Page 210
4.12 Orthogonality property......Page 214
4.13 Hilbert transforms via series expansion......Page 217
4.14 The Hilbert transform of a product of functions......Page 221
4.15 The Hilbert transform product theorem (Bedrosian’s theorem)......Page 224
4.16 A theorem due to Tricomi......Page 227
4.17 Eigenvalues and eigenfunctions of the Hilbert transform operator......Page 235
4.18 Projection operators......Page 239
4.19 A theorem due to Akhiezer......Page 240
4.20 The Riesz inequality......Page 243
and in......Page 251
4.22 Connection between Hilbert transforms and causal functions......Page 255
4.23 The Hardy–Poincaré–Bertrand formula revisited......Page 263
4.24 A theorem due to McLean and Elliott......Page 266
4.25 The Hilbert–Stieltjes transform......Page 271
4.26 A theorem due to Stein and Weiss......Page 281
Notes......Page 286
Exercises......Page 288
5.2 Fourier transform of the Hilbert transform......Page 292
5.3 Even and odd Hilbert transform operators......Page 298
]......Page 301
5.5 Hartley transform of the Hilbert transform......Page 302
5.6 Relationship between the Hilbert transform and the Stieltjes transform......Page 305
5.7 Relationship between the Laplace transform and the Hilbert transform......Page 307
5.8 Mellin transform of the Hilbert transform......Page 309
5.9 The Fourier allied integral......Page 315
5.10 The Radon transform......Page 317
Notes......Page 325
Exercises......Page 326
6.1 Introduction......Page 328
6.2 Approach using infinite product expansions......Page 329
6.3 Fourier series approach......Page 331
6.4 An operator approach to the Hilbert transform on the circle......Page 332
6.5 Hilbert transforms of some standard kernels......Page 336
6.6 The inversion formula......Page 341
6.7 Even and odd periodic functions......Page 343
6.8 Scale changes......Page 344
6.9 Parseval-type formulas......Page 345
6.10 Convolution property......Page 347
6.11 Connection with Fourier transforms......Page 349
6.12 Orthogonality property......Page 350
6.13 Eigenvalues and eigenfunctions of the Hilbert transform operator......Page 351
6.14 Projection operators......Page 352
6.15 The Hardy–Poincaré–Bertrand formula......Page 353
6.16 A theorem due to Privalov......Page 356
6.17 The Marcel Riesz inequality......Page 358
6.18 The partial sum of a Fourier series......Page 363
6.19 Lusin’s conjecture......Page 365
?......Page 368
Exercises......Page 369
7.1 The Marcel Riesz inequality revisited......Page 371
7.2 A Kolmogorov inequality......Page 375
7.3 A Zygmund inequality......Page 380
7.4 A Bernstein inequality......Page 383
7.5 The Hilbert transform of a function having a bounded integral and derivative......Page 390
7.6 Connections between the Hilbert transform on......Page 392
7.7 Weighted norm inequalities for the Hilbert transform......Page 394
7.8 Weak-type inequalities......Page 404
7.9 The Hardy–Littlewood maximal function......Page 408
7.10 The maximal Hilbert transform function......Page 413
7.11 A theorem due to Helson and Szegö......Page 426
condition......Page 428
7.13 A theorem due to Hunt, Muckenhoupt, and Wheeden......Page 435
7.14 Weighted norm inequalities for the Hilbert transform of functions with vanishing moments......Page 442
7.15 Weighted norm inequalities for the Hilbert transform with two weights......Page 443
7.16 Some miscellaneous inequalities for the Hilbert transform......Page 448
Notes......Page 453
Exercises......Page 456
8.1 Asymptotic expansions......Page 459
8.2 Asymptotic expansion of the Stieltjes transform......Page 460
8.3 Asymptotic expansion of the one-sided Hilbert transform......Page 462
Exercises......Page 474
9.2 Hilbert transforms involving Legendre polynomials......Page 478
9.3 Hilbert transforms of the Hermite polynomials with a Gaussian weight......Page 486
9.4 Hilbert transforms of the Laguerre polynomials with a weight function......Page 489
9.5 Other orthogonal polynomials......Page 492
9.6 Bessel functions of the first kind......Page 493
9.7 Bessel functions of the first and second kind for non-integer index......Page 499
9.8 The Struve function......Page 500
9.9 Spherical Bessel functions......Page 502
9.10 Modified Bessel functions of the first and second kind......Page 505
9.12 The Weber and Anger functions......Page 510
Notes......Page 511
Exercises......Page 512
10.1 Some basic distributions......Page 514
10.2 Some important spaces for distributions......Page 518
10.3 Some key distributions......Page 523
10.4 The Fourier transform of some key distributions......Page 527
10.5 A Parseval-type formula approach to......Page 530
10.6 Convolution operation for distributions......Page 531
10.7 Convolution and the Hilbert transform......Page 535
10.8 Analytic representation of distributions......Page 538
10.9 The inversion formula......Page 542
10.10 The derivative property......Page 544
10.11 The Fourier transform connection......Page 545
10.12 Periodic distributions: some preliminary notions......Page 548
10.13 The Hilbert transform of periodic distributions......Page 555
10.14 The Hilbert transform of ultradistributions and related ideas......Page 556
Notes......Page 558
Exercises......Page 559
11.1 Introduction......Page 561
11.2 Alternative formulas: the cosine form......Page 563
11.3 The cotangent form......Page 567
11.4 The inversion formula: Tricomi’s approach......Page 569
0, 1......Page 576
11.5 Inversion by a Fourier series approach......Page 581
11.6 The Riemann problem......Page 583
11.8 The Riemann–Hilbert problem......Page 584
11.9 Carleman’s approach......Page 590
11.10 Some basic properties of the finite Hilbert transform......Page 592
11.11 Finite Hilbert transform of the Legendre polynomials......Page 603
11.12 Finite Hilbert transform of the Chebyshev polynomials......Page 607
11.13 Contour integration approach to the derivation of some finite Hilbert transforms......Page 610
11.14 The thin airfoil problem......Page 617
11.16 The cofinite Hilbert transform......Page 622
Notes......Page 624
Exercises......Page 625
12.1 Introduction......Page 628
12.2 Fredholm equations of the first kind......Page 629
12.3 Fredholm equations of the second kind......Page 632
12.4 Fredholm equations of the third kind......Page 634
12.5 Fourier transform approach to solving singular integral equations......Page 639
12.6 A finite Hilbert transform integral equation......Page 641
12.7 The one-sided Hilbert transform......Page 649
12.8 Fourier transform approach to the inversion of the one-sided Hilbert transform......Page 652
12.9 An inhomogeneous singular integral equation for......Page 654
12.10 A nonlinear singular integral equation......Page 657
12.11 The Peierls–Nabarro equation......Page 658
12.12 The sine–Hilbert equation......Page 660
12.13 The Benjamin–Ono equation......Page 664
12.14 Singular integral equations involving distributions......Page 670
Notes......Page 672
Exercises......Page 673
13.2 The discrete Fourier transform......Page 677
13.3 Some properties of the discrete Fourier transform......Page 680
13.4 Evaluation of the DFT......Page 681
13.5 Relationship between the DFT and the Fourier transform......Page 683
transform......Page 684
13.7......Page 687
13.8 The Hilbert transform of a discrete time signal......Page 689
13.9......Page 692
13.10 Fourier transform of a causal sequence......Page 696
13.11 The discrete Hilbert transform in analysis......Page 700
13.12 Hilbert’s inequality......Page 701
13.13 Alternative approach to the discrete Hilbert transform......Page 706
13.14 Discrete analytic functions......Page 715
13.15 Weighted discrete Hilbert transform inequalities......Page 719
?......Page 720
Exercises......Page 721
14.2 Some elementary transformations for Cauchy principal value integrals......Page 724
14.3 Some classical formulas for numerical quadrature......Page 728
14.4 Gaussian quadrature: some basics......Page 731
14.5 Gaussian quadrature: implementation procedures......Page 734
14.6 Specialized Gaussian quadrature: application to the Hilbert transform......Page 741
and......Page 748
14.8 Numerical integration of the Fourier transform......Page 749
14.9 The fast Fourier transform: numerical implementation......Page 751
14.11 The Hilbert transform via the allied Fourier integral......Page 752
14.12 The Hilbert transform via conjugate Fourier series......Page 753
14.13 The Hilbert transform of oscillatory functions......Page 757
14.14 An eigenfunction expansion......Page 763
14.15 The finite Hilbert transform......Page 767
Notes......Page 770
Exercises......Page 772
Appendix 14.1 Points and weights for quadrature with the function......Page 775
Appendix 14.2......Page 784
33......Page 785
19......Page 786
62......Page 787
9......Page 788
7......Page 789
112......Page 790
50......Page 791
26B......Page 792
74......Page 793
84......Page 794
28......Page 795
161......Page 796
23......Page 797
9......Page 798
53......Page 799
31......Page 800
9......Page 801
56......Page 802
6......Page 803
8......Page 804
25......Page 805
103......Page 806
64......Page 807
105......Page 808
14......Page 809
65......Page 810
4......Page 811
15......Page 812
4......Page 813
8......Page 814
3......Page 815
15......Page 816
44......Page 817
15......Page 818
66......Page 819
43......Page 820
39......Page 821
16......Page 822
30......Page 823
66......Page 824
105......Page 825
44......Page 826
67......Page 827
11......Page 828
22......Page 829
59......Page 830
451......Page 831
72......Page 832
165......Page 833
99......Page 834
24......Page 835
42......Page 836
50......Page 837
13......Page 838
35......Page 839
65......Page 840
65......Page 841
81......Page 842
37......Page 843
53......Page 844
11......Page 845
52......Page 846
112......Page 847
124......Page 848
22......Page 849
66......Page 850
64......Page 851
135......Page 852
20......Page 853
5......Page 854
45......Page 855
322......Page 856
10......Page 857
108......Page 858
35......Page 859
11......Page 860
41......Page 861
34......Page 862
16......Page 863
Author index......Page 864
Subject index......Page 880


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