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| Авторизация |
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| Sheil-Small T. — Complex polynomials |
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| Предметный указатель |
 class 296
 class 271
 classification 273—275
 class 302
 class 282
 class 269 289
 class 289
abc theorem 370
Abel 23
Affine mappings/transformations 5 73
Alander, M. 343
Algebraic function 20
Algebraic polynomial 1
Algebraic tract 103
Analytic continuation lemma 204
Analytic polynomial 1
Angular separation of critical points and univalence 241 243
Angular separation of zeros, convolution theorem 254
Angular separation of zeros, Kaplan class condition 248
Angular separation of zeros, sufficient condition 257
Angular separation of zeros, Suffridge condition 249
Angular separation of zeros, third condition 251
Annihilation property 129
Annular region for zeros 202
Apolar polynomials 180
Apolarity theorem 181
Apolarity, weak 182
Approximate identity 147
Approximation theorem 258
Argument 29
Argument and tangent of curve 387—390
Argument of polynomial with zeros on circle 243
Argument principle 23 27 44 84
Argument principle for Jordan domain 45
Argument principle for meromorphic functions 45
Asymptotic values 15—29
Asymptotic values of finitely valent mapping 90
Asymptotic values of Pinchuk mapping 93—100
Bernstein's inequality 152 186
Bernstein's inequality for trigonometric polynomials 155
Bezout's theorem 4 84
Bisector theorem 200 215 216
Blaschke product 60 193 231 233 351 373
Blaschke product and convex curve 382—387
Blaschke product and harmonic mappings 377—382
Blaschke product and Smale's conjecture 365
Blaschke product and step functions on convex curves 394
Blaschke product, Walsh theorem 377
Blow-up method 13
Bocher — Walsh theorem 192
Bojanov — Rahman — Szynal method 213 226
Bojanov — Rahman — Szynal theorem 215
Bolzano — Weierstrass property 128
Borsuk — Ulam theorem 79
Borwein — Erdelyi extensions 195—196
Borwein — Erdelyi inequality 193
Bound preserving g.c. operator 170
Bound preserving operator 140
Boundary inequality 224
Boundary rotation of curve 389
Bounded boundary rotation 298
Bounded boundary rotation and univalence 389
Bounded convolution operators 142
Bounded convolution operators, integral representation 168
Bounded operator 139
Bounded operator condition 140
Bounded variation 159 221
Branch of algebraic function 21
Branch of inverse function 57
Branch of logarithm 30
Branch of square root 31
Branch point 306
Brannan, D.A. 295
Brouwer's fixed point theorem 48—49
Brouwer's theorem on plane domains 40
Caratheodory's lemma 162
Cauchy — Riemann equations 266
Cauchy's integral formula 128
Cauchy's theorem 24 31 36
Cesaro mean 156—157
Cesaro mean of Kaplan class 301
Cesaro polynomial 300
Chain 36
Change in argument 29
Choquet's theorem 287
circle 73
Circular region 178
Circular region, zeros and critical points 187
Close-to-convex 405
Close-to-convex domain 242
Close-to-convex function 241—242
Closed convex hull 287
Closed under convolution 174
Closing gap problem 112—115
Clunie — Jack lemma 266
Clunie,J.G. 171 266
Cluster set 58
Coefficient 129
Coefficient and maximum modulus, zeros on unit circle 239
Coefficient bound, Kaplan class 294
Coefficient bound, Suffridge class 260
Cohn's reduction lemma 372
Coincidence theorem 47
Compact open topology 128
Comparison principle 19
complex curve 118
Complex form of Bezout's theorem 11
Complex polynomial 1
Composition remark 363
Conical surface 117
Conjugate pair 1
Conjugate polynomial 153
Connected set 30
Constant jacobian 87 105—124
Containment condition, Suffridge convolution theorem 257
Containment lemma 266
Containment property 335
Containment theorem for 286
Containment theorem for 292
Continuation of inverse function 57
Continuity at infinity 83
Continuity of zeros 55
Continuous change in argument 29
Continuous logarithm 28
Convex curve 382
Convex curve and step function 392
Convex domain 78
Convex function 242
Convex function condition 275
Convex harmonic mapping, univalence theorem 391—392
Convex hull 25
Convex in direction of real axis 69
Convex mapping 260
Convex polygon: harmonic univalence criterion 400—401
Convex sequence 157
Convex set 24
Convexity lemma 162
Convexity preserving 141 174 279
Convexity preserving, functions 144
Convexity preserving, g.c. operator 170
Convexity preserving, operators and positive trigonometric polynomials 148
Convexity theory 286—288
Convexity, of level region 360
Convolution 172
Convolution condition, Suffridge angular separation 253
Convolution containment theorem 280
Convolution formula 127
Convolution inequality 279
Convolution inequality for 284
Convolution inequality for 291
| Convolution lemma 269
Convolution of harmonic functions 126
Convolution operator 132
Convolution operator, extension property 141—143
Convolution operator, extension theorem 142
Convolution theorem 279
Convolution theorem for 291
Convolution theorem for 285
Convolution theorem for 292
Convolution theorem, zeros on unit circle 254
Cordova — Ruscheweyh method 361
Craven — Csordas — Smith conjecture 306
Craven — Csordas — Smith conjecture, proof when all critical points real 311
Craven — Csordas — Smith conjecture, proof when exactly 2 non-real zeros 308—310
Craven, T. 306
Critical circle 225
Critical point 24 186 187
Critical point inequality 359
Critical point of Blaschke product 374
Critical point of logarithmic derivative 306
Critical point of logarithmic existence of non-real 307
Critical point of rational function 190
Critical point of real polynomial 305
Critical point of real rational functions, theorem on number of non-real 323—324
Critical point of strongly real rational function 321
Critical point on unit circle, univalence theorem 243
Critical Point Theorem 334
Critical set 66
Cross-cap 123
Csordas, G. 306
CYCLE 36
Cylindrical surface 117
De la Vallee Poussin means 160 301
Degree estimate, Jacobian conjecture 102—104
Degree of function on curve 29
Degree of function on cycle 36
Degree of function on rectilinear polygon 35
Degree of harmonic polynomial 3
Degree of Pinchuk mapping 93
Degree of polynomial 1
Degree of real analytic polynomial 4 83
Degree of trigonometric polynomial 144
Degree principle 31 37
Degree principle for circle 34
Degree principle for homotopic curves 41
Degree principle for rational function 37
Degree principle for simply-connected domain 39
Degree principle for starlike domain 33
Degree principle for triangle 32
Descartes' Rule of Signs 317
Descartes' rule of signs, polynomials with all real zeros 318
Dirichlet means 158
Domain 30
Dual 172
Dual of T(1,1) 271
Duality 172
Duality principle 286
Duality theorem for 275
Duality theorem for 282
Duality theorem for 289
Duality, sums and products 23
Elementary mappings 109
ellipse 73
Enestroem — Kakeya theorem 281
Enestroem — Kakeya theorem, Ruscheweyh generalisation 281
Entire functions of finite order 327
Entire functions with real zeros 343
Erdoes, P. 407
Essential singularity 44
Euler gamma function 239
Extending boundary inequalities 224
Extension property 141
Exterior of curve 34
Extremal distance theorem 221
Extremal polynomial 223
Extremal polynomial, Suffridge 251
Extreme point 287
Extreme point of Kaplan class 293
Fejer means 147
Fejer — Riesz inequality 129
Fermat's last theorem for polynomials 371
Finite limiting value and asymptotic value 19
Finite product duality lemma 175 265 270 282
Finite valence 84
Finite valence and N-fold mapping 390
Finite valence condition 390
Fixed point 48
Fourier coefficient 129
Fourier coefficient of N-fold mapping 391
Fourier series 129
Function of bounded boundary rotation 298
Fundamental group 42
Fundamental group of punctured plane 43
Fundamental theorem of algebra 1 22 26 49—50
g.c. kernel 169
g.c. operator 168
Galois 23
Gamma function 239
Gauss — Lucas Theorem 25 185 189 201
Generalised convolution operator 168 279
Genus of entire function 344
Global homeomorphism condition 58
Global homeomorphism, Jordan domain condition 59
Goodman — Rahman — Ratti theorem 207
Goursat method 32
Grace class 174 253
Grace theorem for rational functions 263
Grace — Heawood theorem 198
Grace — Szegoe theorem 173
Grace — Szegoe theorem, circular regions 179
Grace — Szegoe theorem, linear functionals 177
Grace — Szegoe theorem, proof 176—177
Grace's apolarity theorem 181
Grace's theorem 216 263 282
Grace's theorem, additional forms 183—184
Grace's theorem, applied to Ilieff — Sendov conjecture 208—211
Graph of surface 101
Greatest common divisor 106
Hadamard representation of entire function 344
Harmonic extension 129
Harmonic extension of step function 395
Harmonic extension, containment theorem 396
Harmonic extension, univalence criterion 399
Harmonic function 126
Harmonic function at non-isolated zero 53
Harmonic function, convolution 126
Harmonic function, locally 1-1 64
Harmonic mapping and Blaschke product 377—382
Harmonic multiplication operator 135
Harmonic multiplication operator, class  137
Harmonic multiplication representation 135
Harmonic polynomial 3 50 82
Harmonic polynomial on critical set 66—72
Harmonic polynomial, degree 2 73—78
Harmonic polynomial, theorem on valence 72
Harmonic polynomial, valence near critical set 70—71
Harmonic polynomial, zeros 51 54
Harmonic series 126
Hayman, W.K. 206
Heine — Borel theorem 58
Helly selection theorem 146
Highest common factor 2 110—111
Highest common factor 3 115—117
Hilbert's inequality 130
Homeomorphism 57 81
Homeomorphism of sphere 80
Homeomorphism of unit disc 60
Homeomorphism, condition at infinity 57
Homologous 36
Homology group 42
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