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| Авторизация |
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| Henrici P. — Applied and Computational Complex Analysis (Vol. 3) |
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| Предметный указатель |
 condition 406 477
Aliasing 22
Amplitude characteristic 211
Analytic continuation 153
Annulus 227 229 230 253 445 446 450 451 456 460 461 465 468 469 474 476 478 483 551
Annulus, conjugate function for 470
Antiderivative, symmetric 300
Approximation, by polynomials 521
Area theorem 574 587
Argument, continuous 480 481
Argument, principle of 403 447 449 451 454 482
Askey — Gasper lemma 584 605 610 611
Associate, of analytic function in disk 101 102 107 127 129
Asymptotic expansion, of Fourier coefficient 21
Attenuation factor 22 23 24 26 27 86
Banach space 531 533 534
Barycentric formula 46 47
Bergman kernel function 547 549 551 552 553
Bergman kernel function, real 271 272 492
Bergman kernel function, reproducing property of 271 272 492
Bernoulli’s law 171
Bessel function 25 314
Bessel’s inequality 537
Beta integral 606 607
Bieberbach conjecture 571 576 578 579 580 581 584 587 591 592 602 605 610
Biplane 478
Bit inversion 9
Bluestein algorithm 63
Boundary correspondence 345
Boundary correspondence function 379 391 415 463 475 476
Boundary correspondence function, exterior 381 385 392 396
Boundary correspondence function, interior 380 382 392 393
Boundary correspondence function, inverse 402 403 420 421
Boundary correspondence function, inverse, normalized 402 404
Boundary integral method 287
Boundary representation formula 257 269
Boundary value problem, for function analytic in disk 102
Boundary value problem, for function analytic in upper half-plane 197
Burniston and Siewert, method of 183 187 191 192
Capacitance 442
Capacity, of Jordan curve 374 379 385 392 552
Caratheodory — Fejer approximation 528
Carathtodory convergence theorem 543 588 591
Carrier frequency 206
Casorati — Weierstrass theorem 237
Cauchy integral 88 91 92 100 101 102 107 109 123 129 132 137 140 150 151 159 164 165 184 278 279 282 387 393
Cauchy integral on closed curve 113
Cauchy integral on real line 193
Cauchy integral on straight line segment 136
Cauchy integral, behavior near terminal point 151
Cauchy integral, discrete 109 110 111 112
Cauchy integral, numerical evaluation of 108
Cauchy kernel 126 561
Cauchy — Riemann equations 39 215 489 495
Cauchy’s estimate 20 31 519 580
Cauchy’s formula 87 99 113 114 117 133 290 364 380 401 461 502 554 566 567 578
Cauchy’s Theorem 153 160 198 289 290 474
Channel, periodic 469
Chebyshev polynomial 148 231 374 546
Clausen’s formula 606 607 610
Clenshaw algorithm 35 142
Coefficient, of error propagation 12 14
Composition of formal Laurent series 508
Composition of formal power series 76
Condition 9 10
Conjugate gradients 314 416 422
Conjugation operator 40 42 50 104 106 131 400
Conjugation operator, norm of 105
Connectedness 221 240 356
Continuation, continuous 122 164 167 177 233 235
Continuation, harmonic 232 233 235 237
Continued fraction 137 138 141 142 150
Convergence acceleration 21 27
Convergence, locally uniform 241
Convergence, quadratic 420
Convergence, topological 592
Convolution 55 57 58 60 62 175 180
Convolution theorem 56 57 61 63 70 84 315
Convolution theorem for Fourier transform 200 210
Convolution, one-sided 64 65
Covariance function 59
Crescent map 331
Cross ratio 443
Crosscut 347 348 350 352 437
Crowding 428
Curvature 282 489 491
Curve, nomotopic 218
Curve, simple 88
Derivative, of formal Laurent series 508
Difference equation 141
Differentiation of interpolating polynomial 52
Differentiation, Numerical 32 54
Dilatation measure 329 331 333 334 338
DIMENSION 535
Dini’s formula 267 268 287
Dini’s theorem 556
Dipole 277
Dirichlet integral 313 314 433 434 435 456
Dirichlet problem 39 223 224 225 227 228 229 243 246 247 248 258 266 270 279 285 370 371 373 374 375 377 378 451 452 457 461 470 471
Dirichlet problem, generalized 244 245
Discretization 303
Distortion theorem 577
Division, of polynomials 79
Dixon’s theorem 610
Eigenvalue 285
Eigenvalue problem 310
Eigenvalue, multiplicity of 285
Electroencephalography 59
Electrostatics 250 264 323 371 454 455 483
ellipse 118 231 263 391 392 412 441 455 546 550
Equiconvergence 140 151
Euler’s constant 527
Euler’s first identity 609
Expansion theorem 311 314 319 322
Exponent, characteristic 611
Exponential series 77
Faber coefficient 514 515 516
Faber coefficient, in Faber series 519
Faber function 514 585
Faber polynomial 507 512 513 516 517 184 585
Faber series 518 519 522 527 543
Faber series, truncated 521
Faber transform 528 529
Faber transformation 573 575
Family, normal 326 594
Fast Fourier transform (FFT) 2 9 13 14 16 25 33 34 36 58 59 110 146 202 227 230 267 314 393 405 413 473 477 520
Fast Fourier transform in geophysics 63
Fast Fourier transform, matrix interpretation of 15
Fast Poisson solver 314 321 457
Fine-tuning 33 35
Finite differences 303 309 314 317 322 427
Finite elements 305 308 314 320 321 427 435
Fonder coefficient 17 20 21 22 25 31 227 230 390 392 405 411 414 415 471 477 536
Fonder coefficient, discrete 28 109
Fonder coefficient, trapezoidal value of 17 20
Formula, asymptotic 154 162 191 527
Fornberg’s method 414 422 478 506
Fourier analysis, discrete 1 6 28 60
Fourier analysis, multivariate 80 86
Fourier integral theorem 27 200
Fourier operator, discrete 2 5 6 10 81
Fourier operator, inverse 320
Fourier series 260 266 267 373 389 393 410 472 536 538 540 541 543 548 563
Fourier synthesis 24
Fourier transform 200 201 203 207
Fourier transform, discrete 6 14 28 32 37 317 318 319 320 322 411 416 419
Fourier transform, inverse 202 205 210
Fredholm alternative 284 398
Frequency admittance 211
Fubini’s Theorem 181
| Function, biharmonic 302
Function, complex-differentiable 288
Function, conjugate harmonic 39 216 217 219 223 371 379 386 407 448 449 452 465 471 494
Function, conjugate periodic 40 41 42 104 323 402 413
Function, conjugate periodic, exterior 408
Function, conjugate periodic, for annulus 470
Function, elliptic 377 480
Function, generating 33
Function, harmonic 214 215 216 217 219 222 230 245 258 274
Function, hypergeometric 99 160 163 604 605 609
Function, orthonormal 311
Function, piece wise polynomial 308
Function, rational 53 186 237
Function, subharmonic 243
Function, univalent 571 584
Function, vanishes regularly 196
Functional 307 313 491 492 591
Fundamental solution 255 256 296 370
Fundamental solution, normalized 255 269 270
Gamma function 38
Gaussian rule, for numerical integration 17 426
Gaussian rule, for numerical integration, compound 426
Gaussian sum 14
Geiger’s algorithm 36 38 39 78
Geneva effect 428
Gradient, complex 277 296 299 454
Graeffe’s method 67 69 71
Gram — Schmidt algorithm 535 542 547 549 553 555
Green’s formula 256 265 272 306 434 545 585
Green’s function 257 258 259 260 270 302 547 551
Grid generation 324 444
Group velocity 212
Growth theorem 578 590 594
Grunsky inequality 586
Grunsky series 515 517 585 586
Hadamard product 54 57 62 63
Hadamard product in  84 317
Hadamard three-circle theorem 254
Harmonic function, positive 238
Harmonic function, sequence of 241
Harnack’s inequality 238 239 240 343
Harnack’s theorem 239
Harnack’s theorem for analytic functions 242 336
Heat flow 265
Helmholtz equation 321
Hilbert problem 119 120 122 123 125
Hilbert reciprocity relations 105 118
Hilbert space 533 534 538 539 548 549 569
Hilbert transform on circle 103 104 111 112 113 144 145 149
Hilbert transform on real line 193 197 198 199 201 203 205 207 212
Hilbert transform on real line, numerical evaluation of 202
Holder condition 91 92 95 98 99 125 156 157
Holder condition, at  194 197
Holder condition, exponent of 91
Holder condition, uniform 91 101
Holder continuity 127 128 155 156 164 166 168 169 178 188 189 193 194 195 224 278 279 280 281 285 286 386
Holder’s Inequality 275 276
Homeomorphism 345 346 379
Horner algorithm 10 12 14
Hurwitz, theorem of 326 338 589
Ill-conditioning 470
Image, circular 488 498
Image, degraded 85
Independence, linear 534
Index vector 80
Index, of function on curve 120 121 122 134
Inner product 306 533 534
Inner product space 306 567
Instability, numerical 141
Integral equation of Abel 174 175 176 178 182
Integral equation of Banin 397
Integral equation of Berrut 398 401
Integral equation of Carleman 174 176 178 182
Integral equation of Fredholm type 281 282
Integral equation of Gerschgorin 395 468 469 470
Integral equation of Kantorovich — Krylov 397
Integral equation of Kerzman and Trummer 560 561 562 563 569
Integral equation of Lichtenstein 401
Integral equation of potential theory 279
Integral equation of Symm 323 377 378 381 382 388 389 393 399 400
Integral equation of Symm for exterior map 379 385 386 388
Integral equation of Theodorsen 404
Integral equation of Theodorsen for exterior map 408
Integral equation of Theodorsen — Garrick 474 476
Integral equation of thin airfoil theory 170 171 174 182 183
Integral equation of Timman 410
Integral equation of Warschawski 395 401 402 466 469
Integral operator 399
Integral, indefinite 216 217 219 222
Integral, singular 43
Integration, symbolic 300 303
Interpolating polynomial, balanced trigonometric 26
Interpolation 371
Interpolation by spline functions 25 26 389
Interpolation, linear 24
Interpolation, trigonometric 43 52
Interpolation, trigonometric, osculatory 52
Jacobi polynomial 149
Jacobi triple product identity 262 263 486
Jordan curve 256 282 284 286 296 348 350 352 365 370 374 375 389 402 407 414 446 456 488 497 503 519 521 552 568 574 588 590 596
Jordan curve theorem 120
Jordan curve, analytic 451
Jordan curve, piecewise analytic 357 388 399 409 454 476 524 525 545
Jordan curve, piecewise analytic, admissible 399 401
Jordan curve, piecewise analytic, corner of 357
Jordan region 128 259 280 296 346 348 356 357 370 436 549 553
Joukowski map 455 546 572 575 576
Keldysh and Sedov, problem of 204 205
Kernel of sequence of regions 588 589
Kernel, reproducing 548
Kernel, skew-hermitian 561 570
Kernel, transposed 285
Koebe  theorem 334 504 576 578 596
Koebe family 329 339 341 344 457
Koebe function 326 327 328 333
Koebe map, in theory of univalent functions 573 575 576 578 579 598 610
Koebe’s algorithm, for constructing circular map 497 498 500 505 506
Komatu’s method 460 505
Lagrange — Burmann formula 78 510 511 513 593
Laguerre polynomial 34 150
Landau — Valiron theorem 366 369
Laplace transform 175 180 202
Laplace transform, numerical inversion of 33 38
Laurent coefficient 20 31 32 33 36 37 510 523
Laurent series 31 36 114 180 185 190 192 471 572 585
Laurent series, formal 507
Laurent series, formal, almost regular 510 512
Laurent series, formal, at 507 508 515
Laurent series, formal, singular 509
Lebedev — Milin inequality 581 583 592 601
Lebesgue — Wolff lemma 348 350 352
Legendre polynomial 143 144 149
Lehmer method 36
Lindelof — Caratheodory theorem 355 363 366 368
Liouville’s equation 294
Liouville’s theorem 124 325 596
Liouville’s theorem for harmonic functions 242
Lipschitz class (Lip) 91 96 97 100 101 104 105 114 141 146 147 155 156 159 183 278
Loewner’s differential equation 592 594 598 599
Majorization, principle of 252 253
Map, angle preserving 354
Map, circular 488 496 497
Map, circular, of Koebe 444 497
Map, conformal 323 427
Map, topological 345 347
Mapping function, exterior 374
Matrix 308
Matrix, circulant 62
Maximum, principle of 221 222 254 347 496 596
Maximum, principle of, generalized 244
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