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Henrici P. — Applied and Computational Complex Analysis (Vol. 3)
Henrici P. — Applied and Computational Complex Analysis (Vol. 3)

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Название: Applied and Computational Complex Analysis (Vol. 3)

Автор: Henrici P.

Аннотация:

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 637

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\varepsilon$ 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 $\Pi_n$      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 $\infty$      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 $\frac14$ 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 $\infty$      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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