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Hayman W.K. — Multivalent Functions
Hayman W.K. — Multivalent Functions

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Название: Multivalent Functions

Автор: Hayman W.K.

Аннотация:

Multivalent and in particular univalent functions play an important role in complex analysis. Great interest was aroused when de Branges in 1985 settled the long-standing Bieberbach conjecture for the coefficients of univalent functions. The second edition of Professor Hayman's celebrated book is the first to include a full and self-contained proof of this result, with a new chapter devoted to it. Another new chapter deals with coefficient differences of mean p-valent functions. The book has been updated in several other ways, with recent theorems of Baernstein and Pommerenke on univalent functions of restricted growth and Eke's regularity theorems for the behaviour of the modulus and coefficients of mean p-valent functions. Some of the original proofs have been simplified. Each chapter contains examples and exercises of varying degrees of difficulty designed both to test understanding and to illustrate the material. Consequently the book will be useful for graduate students and essential for specialists in complex function theory.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 263

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A(p,\lambda)$, $A(p,\beta,\lambda)$      73
$A_0$      38
$A_1$, $A_2$      84
$A_1(p,\beta)$      71
$A_2$      1 162
$a_3$      215
$a_4$, $a_6$      230
$A_5$      161 230
$A_k$      243
$a_n(\lambda)$      221 247
$B_f$      200
$B_{t’t"}$      208
$b_{\lambda}(z)$      26
$C_0$      61
$c_k$, $c_k(0)$, $c_k(t)$      237
$c_n(t)$      216
$D(\theta_0)$      61
$D_F$      128
$D_k$      243
$d_n(\lambda)$      26 243
$E_1$, $E_2$      86
$f(z,t)$      210
$f_k(z)$      95 161
$f_n(z)$      20
$G(\theta)$      240
$g_n(t)$      239 242
$g_t(z)$      207
$g_t(\zeta)$      215 237
$h(z,t)$      237
$H^+(R)$      39
$I_1(r,f)$      9
$I_D(u)$      109
$I_G(r,f)$      11
$I_{\lambda(r,f)}$      27 67
$l_f$      147
$n(w,\Delta,f)$      144
$p(R, \Delta, f)$      29
$P_n(z)$, $P^k_n(z)$      231
$r_0$, $r_0^{\ast}$      126
$R_f$      131
$R_n$      19
$S_0$      36
$S_f$      200
$S_G(r,f)$      78
$S_{t’t"}$      208
$S_{\lambda}(r)$      69
$u^{\ast}(z)$      117
$\alpha$      9 45 50 150
$\alpha(r)$      64
$\alpha(\theta)$      18
$\alpha(\zeta)$      42
$\alpha_0$      45
$\alpha_n$      20
$\bar{D}$      104
$\beta$      55 66 200 209
$\beta(0)$, $\beta(t)$      209
$\beta_0$      79
$\Delta$      20 33 163
$\delta_f$      200
$\Delta_n(\varepsilon)$      19
$\Delta’$      20
$\gamma$      82
$\Gamma(x)$, the gamma function      26 151
$\gamma_t$, $\gamma_{t’t"}$      207
$\kappa(t)$      210
$\lambda(t)$      207
$\Lambda_k^n(t)$      235
$\mathfrak{B}$      143
$\mathfrak{B}_0$      137
$\mathfrak{M}$      141
$\mathfrak{S}$      1
$\mathfrak{S}_0$      6 149
$\mathfrak{S}_1$      82 197 204
$\mathfrak{S}_2$      82
$\mu$      33 172 180
$\mu_q$      28
$\nabla^2u$      77 107 169
$\omega(R)$      51
$\omega(z)$      109 243
$\Omega(\delta)$      117
$\omega^{\ast}(z)$      119
$\Sigma_k$      242
$\tau$      209
$\theta(\sigma)$      30
$\xi_1(R)$, $\xi_2(R)$      51
2-point estimate      176
A(p), $A(p,\beta)$      66
A(p,b,c)      100
A(p,k,N)      99
A(r,f)      27
Admissible domain      109
Analytic domain      104
Areally mean (a. m.) p-valent      144
Argument of f(z)      224
Argument of f’(z)      226
Asymptotic behaviour      19 60 154 155
Asymptotic behaviour of coefficients      15 64 151 156
Averaging assumptions      19 37 144
B      136
Bieberbach’s conjecture      xi 4 230
Bloch functions      143
Bloch’s constant      136
Bloch’s theorem      136
Bounded univalent functions      78
C, $C_1$, $C_2$,...      172
C. A. x      7 103
Circumferentially mean (c. m.) p-valent      144
Coefficients of univalent functions      9 15 247
Coefficients of univalent functions, of mean p-valent functions      65 131
Condenser, capacity of a condenser      109
Connectivity      104
Convex domain      11
Convex function      70
Convex univalent functions      11 12
Correspondence of points under a transformation      200
D, $D^{\ast}$      115
de Branges’ theorem      xi 230
Dense subclass      197
Diameter      199
Dirichlet’s minimum principle      109
Dirichlet’s minimum principle, problem of Dirichlet      108
Distortion theorems      4 28
Domain      104
Functions of maximal growth      16 17 45
Functions of maximal growth with k-fold symmetry      95 159 185
Functions of maximal growth without zeros      145 159
Functions of maximal growth, zero at the origin      61 64 148 158 165
G(R)      77 170
G(t)      207
g(z,t)      210
Gauss’ formula      105
Goodman’s conjecture      xi 163
Green’s formula      106 169
Green’s function      122
H(R)      37
h(z, t’,t")      208
I(E)      84
I(z)      239
Inner radius      124
Inverse function      222
k-symmetric      95 185
Koebe function      2
l(R)      29 199
Landau’s theorem      143
Lebesgue integral      31
Legendre polynomials      231
Legendre polynomials, associated Legendre functions      231
Legendre’s addition theorem      232
Length-area principle      29
Lipschitzian, Lip      104
Lowner’s differential equation      197
M(r,f)      8 33
Major arc      16 19 154
Maximal growth      45
Mean p-valent      xi 38 64 165
Milin’s conjecture      230 236
Minor arc      16 21 153
Modules, theory of      xi 229
Modulus of continuity      116
Modulus of doubly connected domain      110
n(r, w)      67
n(w)      29 144
O, $O^{\ast}$      113
Odd univalent functions      161 186 248
Omitted values      3 94 150
Order (of f(z) at $\zeta$)      42
P(R)      29 67 144
p(r, R)      67
p-valent      xi 1 28 163
Power series      243
Power series with gaps      98 99 101
Principal frequency      103
Radius of convexity      226
Radius of greatest growth (r. g. g.)      17 48
Radius of starshapedness      227
Real coefficients      13 162 220
Regularity theorems      xi 16 49 150
Riemann’s mapping theorem      44 204
Robertson’s conjecture      249
Rogosinski’s conjecture      250
Rouche’s Theorem      147
S      22 36
S(R)      22
Schwarz’s inequality      30
Schwarz’s lemma      11
Schwarz’s reflection principle      44
Slit      204
Slit, sectionally analytic slit      198
Starlike domain      14
Starlike univalent function      14 188
Steiner symmetrization      112
Stolz angle      22
Subordination      250
Symmetrization      112
Symmetrization of condensers      119
Symmetrization of functions      116
Symmetrization, circular or Polya’s      113
Symmetrization, principle of      127
Szego’s conjecture      95
Torsional rigidity      103
Transfinite diameter      103
Transformation      200
Transformation, infinitesimal transformation      203
Typically real      13
Univalent      xi 1
Variational method      xi 229
Vitali’s convergence theorem      21
W(R)      37 76
[B] for Burkill [1951]      31
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