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| Hahn L.- Sh., Epstein B. — Classical Complex Analysis |
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| Предметный указатель |
1/4-theorem 333
Abel, N.H.(1802-1829) 34 372
Abel, N.H.(1802-1829), continuity theorem 37 67
Abel, N.H.(1802-1829), power-series theorem 34
Abel, N.H.(1802-1829), transformation 69
Absolute value 5
Analytic continuation 280
Analytic continuation, direct 283
Apollonius (262?-200? B.C.), Apollonius circle 96 191
Approximate identity 371
Arc, closed 105
Arc, rectifiable 106
Arc, simple 105
Arc, smooth 107
Arc, smooth, piecewise 107
Argument 7
Argument principle 168 184 217
Argument, principal 56 172 184
Artin, E.(1898-1962) 304
Arzela, C.(1847-1912), Ascoli — Arzela theorem 323 334
Ascoli, G.(1843-1896) 323 334
Axis, imaginary 6
Axis, real 6
Banach, S.(1892-1945) space 136 385
Bergman, S.(1895-1977) 406
Bergman, S.(1895-1977) space 406
Bessel, F.W.(1784-1846) 71
Bieberbach, L.(1886-1982) 332
Bieberbach, L.(1886-1982), area theorem 331 333 355 358
Bieberbach, L.(1886-1982), conjecture 333
Bijection 4 9 10 48 85 88 337 338
Blaschke, W.(1885-1962) 43 235 201
Blaschke, W.(1885-1962), product 192 238 245 256
Bloch, A.(1893-1948) 388 389
Bloch, A.(1893-1948), constant 392
Boas, R.(1912-1992) 134
Bohr — Mollerup theorem 307 309 321
Bohr, H.(1887-1951) 306
Bolzano, B.(1781-1848), Bolzano — Weierstrass theorem 19 43 323 324 326
Borel, E.(1871-1956) 27 32 288
Borel, E.(1871-1956) measure 372 382
Branch 293
Branch point 291 294 317
Branch point, order of 294
Brouwer, L.E.J.(1881-1966) 105
Canonical product 242 308
Cantor, G.(1845-1918) 28
Cantor, G.(1845-1918), intersection theorem 28 63 116 132 301
Caratheodory, C.(1873-1950) 205 338 342 383
Cardioid 360
Casorati, F.(1835-1890), Casorati — Weierstrass theorem 147 179 397
Cauchy, A.L.(1789-1857) 75
Cauchy, A.L.(1789-1857), Cauchy — Goursat theorem 28 113 120 127 128 132 161 299 303 352
Cauchy, A.L.(1789-1857), Cauchy — Hadamard formula 34 44
Cauchy, A.L.(1789-1857), Cauchy — Riemann equations 75 79 97 98 100 114 363
Cauchy, A.L.(1789-1857), criterion, infinite product 225 233
Cauchy, A.L.(1789-1857), criterion, sequences 18
Cauchy, A.L.(1789-1857), criterion, series 22
Cauchy, A.L.(1789-1857), criterion, uniform convergence 30
Cauchy, A.L.(1789-1857), estimate 122 135 276 341 388 389 396
Cauchy, A.L.(1789-1857), inequality 13
Cauchy, A.L.(1789-1857), integral formula 119 133 139 156 185 244 254 326 366 381
Cauchy, A.L.(1789-1857), principal value 157
Cauchy, A.L.(1789-1857), product series 23 68 130
Cauchy, A.L.(1789-1857), residue theorem 154 165 295
Chain rule 44 80 100
Christoffel, E.B.(1829-1900) 353
Collinear points 13
Complex plane 5
Complex plane, extended 10
Component (connected) 28 260 268
Conformal mapping 85 86 188
Conformally equivalent regions 337
Connected set 28 73
Connected set, multiply 124 353
Connected set, polygonally 28
Connected set, simply 124
Convergent series, absolutely 22
Convergent series, conditionally 22
Convergent series, locally uniformly 31
Convergent series, uniformly 30
Convolution 384
Courant, R.(1888-1972) 338
Covering, finite covering 27
Covering, open covering 27
Covering, subcovering 27
Critical line 232
Cross ratio 91 102
Curve 144
Curve, exterior of 114
Curve, interior of 114
de la Vallee Poussin, C.J.(1866-1962) 232
deBranges, L.(1932-) 333
DeMoivre, A.(1667-1754) 8
Dilation 89 101 187
Dirichlet, P.G.L.(1805-1859) discontinuous factor 163
Dirichlet, P.G.L.(1805-1859) problem 373 383
Dirichlet, P.G.L.(1805-1859) series 24
Disc 26
Disc, Doetsch, G.(1892-1977) 197
Doetsch three-line theorem 197
Duhamel principle 111
Entire function 47 61 67 123 149
Entire function, finite order 250
Entire function, rational 150
Entire function, transcendental 150 400 405
Equicontinuous family 323
Equivalence relation 284 337
Euclid (330?-275? B.C.) 229
Euler, L.(1707-1783) 14 51 229 244 302 304 308 319
Euler, L.(1707-1783) beta function 309
Euler, L.(1707-1783) constant 307
Euler, L.(1707-1783) gamma function 302 351
Euler, L.(1707-1783) identity 231
Exponent of convergence 253 275
Exponential function 47
Faber, G.(1877-?) polynomial 267
Fabry, E.(1856-1944) 287
Fatou, P.(1878-1929) 288 328 372 405
Fejor, L.(1880-1959), kernel 384
Fibonacci (11747-1250?) 66 405
Field 2
Field, subfield 2
Fixed point 90 103 183
Fourier, J.B.J.(1768-1830) 163 183 370 373 374 384
Fourier, J.B.J.(1768-1830) coefficient 384
Fourier, J.B.J.(1768-1830) transform 183
Fresnel, A.J.(1788-1827) 165
Friedrichs, K.O.(1901-1983) 371
Friedrichs, K.O.(1901-1983), mollifier 371
Function element 283
Fundamental theorem of algebra 60 61 72 123 134 150 175 183 204 259
Funktion im Grossen 283
Gauss, C.F.(1777-1855) 60 132
Gauss, C.F.(1777-1855) formula 307
Gauss, C.F.(1777-1855) mean-value theorem 132 185 381
Gauss, C.F.(1777-1855) multiplication formula 320
Gauss, C.F.(1777-1855), Gauss — Green theorem 132
Gauss, C.F.(1777-1855), Gaussian integer 268 271
Gauss, C.F.(1777-1855), Gaussian plane 5
Geometric series 32
Goursat, E.(1858-1936) 113 122 127 132 161 299 303 352
Green, G.(1793-1841) 114 376
Green, G.(1793-1841) function 376
Green, G.(1793-1841) identity 379
Green, G.(1793-1841) theorem 114 364
Group 88 101
Group, unimodular 103
Hadamard, J.(1865-1963) 232
Hadamard, J.(1865-1963) factorization theorem 254
| Hadamard, J.(1865-1963) gap theorem 285 315
Hadamard, J.(1865-1963) three-circle theorem 194
Hamack, C.G.A.(1851-1888) 374
Hamack, C.G.A.(1851-1888) inequalities 375
Hardy, G.H.(1877-1947) 232
Harmonic function 80 97 244 363
Harmonic function, conjugate 80 98 363 365
Heine, H.E.(1821-1881), Heine — Borel theorem 27 32 288
Hewitt, E.(1920-) 27
Hilbert, D.(1862-1943) 338 373
Hoelder, O.(1859-1937) 304
Hoffman, K.(1930-) 328 373
Hurwitz, A.(1859-1919) 173 184 330
Hyperbolic function 54
Implicit function theorem 83
Infinite product 223
Infinite product, locally uniform convergence of 233
Jacobi, C.G.J.(1804-1851), Jacobian 83
Jensen, J.L.W.(1859-1925) formula 245 249 275 383
Jensen, J.L.W.(1859-1925) inequality 257
Jentzsch, R. 174 329
Jordan, C.(1838-1922) 103 113 342
Jordan, C.(1838-1922) curve 103 383
Jordan, C.(1838-1922) inequality 161
Joukowski aerofoil 344
Julia, G.M.(1893-1978), Julia direction 401
Koebe,P.(1882-1945) 333 338 342 359
Koebe,P.(1882-1945) function 333 334 345
l'Hopital's rule 99
Lacunary series 285
Lagrange, J.L.(1736-1813) identity 12
Lagrange, J.L.(1736-1813) interpolation formula 181
Landau, E.(1877-1938) 396 400
Laplace, P.S.(1749-1827), equation 80 82 86 363
Laplace, P.S.(1749-1827), operator 100
Laplace, P.S.(1749-1827), transform 136
Laurent, P.A.(1813-1854) 141 145 148 152 260 265 354
Lebesgue, H.L.(1875-1941) 368 372 383
Legendre, A.M.(1752-1833) duplication formula 321
lim inf 20
lim sup 20
Limit, non-tangential 37 39 327 373
Limit, radial 327 336 372
Lindeloef, E.L.(1870-1946) 196 199 338
Linear approximation 83
Linear part 83
Liouville, J.(1809-1882) 55 123 134 150 151 213 338 388 397
Logarithmic derivative 167 217 233 242 256
Logarithmically convex function 194 197 305 309 320
Majorant 32
Maximum and minimum modulus principle 58 72 122 124 135 185 261 366 378 399
Mean-value theorem 77 99 364 380
Mean-value theorem, Gauss mean value theorem 132 185 381
Menshoff, D.(1892-) 76
Meromorphic function 172 180 207 267 399
Mertens, F.C.J.(1840-1927) 24
Metric 10 137 323
Minimum modulus principle 72
Mittag — Leffler, G.M.(1845-1927) 208 260 267 274 404
Modular function 387
Moebius, A.F.(1790-1868), Moebius transformation 87 189 204 275 288 334 337 340 342 346 360 367 378
Mollerup, J. 306
Monodromy theorem 28 300 340 352 377 387
Montel, P.A.A.(1876-1975), Montel selection theorem 325 334 335 341 355 382
Mordell, L.J.(1888-1972) 285
Morera, G.(1856-1909) 127 136 298 303 335 383
Multiplicity of a pole 145 168 250 271
Natural boundary 223 283 315 405
Neighborhood 26 149
Neumann, C.(1832-1925) 338
Nevanlinna, R.(1895-1980) 249 400
Nevanlinna, R.(1895-1980), Nevanlinna class 275
Norm 136
Norm, supremum 199 385
Normal family 326 355
Number, complex conjugate 3
Number, imaginary part of 3
Number, purely imaginary 3
Number, real part of 3
Open mapping theorem 176 184 340
Order of a branch point 294
Order of a pole 145 149 153
Order of a rational function 152
Order of an entire function 250
Ostrowski, A.(1893-?) 275 287
Over-convergence 287
Painleve, P.(1863-1933) 299 338
Parallelogram law 12
Parseval, M.A.(1755-1836), equality 135 384 385
Partial fraction 152
Peano, G.(1858-1932) 105
Periodic function 53
Permanence, law of 301 307 311 318
Phragmen, L.E.(1863-1937) 196 199
Picard, C.E.(1856-1941) 147 259 387 397 401
Poincare H.(1854-1912) 103 292 338
Point, accumulation 27 208 217 267 271 323 404
Point, at infinity 10
Point, branch 294 295 297
Point, fixed 90 103
Point, isolated 27
Poisson, S.D.(1781-1840), integral formula 133 368 385
Poisson, S.D.(1781-1840), kernel 98 250 368 382
Poisson, S.D.(1781-1840), Poisson — Jensen formula 383
Pole 145
Pole, logarithmic 376
Pole, simple 154
Polya, G.(1887-1985) 64 66 70 288 403 405
Power series 34
Power series, center of 34
Power series, circle of convergence 35
Power series, radius of convergence 34
Prime number theorem 232
Principal logarithm 57
Principal part 144 148
Principal value 57 291
Pringsheim, A.(1850-1941) 284
Ptolemy, K.(85?-165?) 14
Ratio Test 36
Reciprocation 89 101 340
Reflection 93 298
Region 28
Region, multiply connected 124 337 353
Region, parallel-slit 354
Region, simply connected 124 266 337
Region, Stolz 37
Residue 153
Riemann, G.F.B.(1826-1866) 23 120 145 147 338 363 399
Riemann, G.F.B.(1826-1866), hypothesis 232
Riemann, G.F.B.(1826-1866), mapping theorem 327 338
Riemann, G.F.B.(1826-1866), sphere 10 18 87 103 183 337
Riemann, G.F.B.(1826-1866), sum 108 335
Riemann, G.F.B.(1826-1866), surface 293
Riemann, G.F.B.(1826-1866), zeta function 232
Riesz — Thorin interpolation theorem 198
Riesz, M.(1886-1969) 198
Riesz, M.(1886-1969), Rouche, E.(1832-1910) 174 184 329 330 389
Runge, C.D.T.(1856-1927), approximation theorem 260 266
Schlicht function 174 329
Schoenberg, I.J.(1903-?) 396
Schottky, F.H.(1851-1935) 392 398 400
Schwarz,H.A.(1843-1921) 72 316 338
Schwarz,H.A.(1843-1921), lemma 72 187 204 339 341 388
Schwarz,H.A.(1843-1921), Schwarz — Christoffel formula 253
Schwarz,H.A.(1843-1921), Symmetry principle 298 360
Set, boundary of 27
Set, bounded 27
Set, closed 26 63
Set, closure of 26
Set, compact 27 63
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