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Caratheodory C. — Theory of Functions of a Complex Variable. Volume 2
Caratheodory C. — Theory of Functions of a Complex Variable. Volume 2



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Название: Theory of Functions of a Complex Variable. Volume 2

Автор: Caratheodory C.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1954

Количество страниц: 220

Добавлена в каталог: 21.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accessible boundary arc      100
Angular derivative      28 ff. 32
Angular derivative and zeros      34 ff.
Angular derivative, theorem on      32
Automorphic function      74 186
Bi-cylinder      113
Boundary arc, accessible      100
Boundary arc, free      99 100 102
Boundary, mapping of      88 ff. 102
Canonical covering surface      83
Caratheodory, C.      48 117 208 215
Cayley, A.      130
Circular-arc triangles, mapping of      129 ff. 162
Conformal mapping      52 ff.
Congruence transformations      72 73
Connecting formulas      155 ff.
Contiguous hypergeometric functions      141
Corners, mapping at      104 ff.
Covering surface (universal)      71 80
Covering surface (universal), canonical      83
Crescent      52
Dieudonne, theorem of      19
Differential equations      123
Differential equations, systems of      127 ff.
Dihedral class      175
Distortion theorems      20 62
Doubly-connected regions, mapping of      69 ff.
Ecart      113
Elementary mappings      52 ff.
Equivalent points      73
Essential singularities      195 ff.
Essential singularities of meromorphic functions      205 ff.
Essential singularities of the first (second) kind      212
Euler, L.      137
Faber      62 68
Fatou's theorem      43 48
Fatou, P.      43
Fejer, L.      97
Free boundary arc      99 100 102
Frontier point, accessible      99
Function of bound one      11
Function of several complex variables      113 ff. 120
Function of two complex variables      113 ff. 119
Function, automorphic      74
Function, bounded      11 ff. 18 114
Function, modular      173 ff. 187 189
Function, Schwarz's triangle      173 ff.
Function, unit      12
Fundamental region      83
Gauss's hypergeometric series      138
Gauss, C.F.      137 141 143
Group of congruence transformations      73 ff.
Hartogs, F.      114
Hartogs, F., theorem of      114 ff.
Homotopic      59
Hypergeometric differential equation      135 ff. 137 149
Hypergeometric series      138
Icosahedral class      176
Jensen's theorem      22
Jensen, J.L.      22
Julia's theorem      27
Julia, G.      27
Koebe — Faber distortion theorem      62 ff. 68
Kummer's differential equation      143 ff.
Kummer's integrals      148 ff.
Kummer, E.E.      144
Landau's theorem      197
Landau, E.      195
Landau, E., radius      196
Lebesgue integral      43
Lebesgue, H.      215
Lebesgue, H., theorems of      47 49 50
Lens      52
Lindeloef, E.      11
Lindeloef, E., two theorems of      42 ff.
Loewner, theorem of      34
Mapping at a corner      104 ff.
Mapping of doubly-connected regions      69 ff.
Mapping of nested annular regions      84 ff.
Mapping of Schwarz (circular-arc) triangles      129 ff. 162 173 181
Mapping of the boundary      88 ff. 102
Mapping of the interior of a Jordan curve      92 ff.
Mapping, conformal      52 ff.
Mapping, elementary      52 ff.
Mapping, quasi-conformal      53
Meromorphic functions      205 ff.
Milloux's theorem      107 ff. 109
modular configuration      184 ff.
Modular configuration, function      173 ff. 187 189
Modular configuration, triangle      187
Modulus of a doubly-connected region      73
Montel's theorem      201 ff. 203
Montel, P.      203
Natural boundary      186
Nevanlinna, R.      118
Normal sequence of discs      208
Octahedral class      176
Picard's first theorem      199
Picard's second theorem      203
Picard, E.      195
Pick's theorem      14 ff. 23
Poisson's integral, an application of      38
Poisson's integral, generalization of      49
Poly-cylinder      121
Quasi-conformal mapping      53
Reflection in an analytic curve      101
Reflection principle (of Schwarz)      88 ff. 101 211
Riemann mapping theorem      54 ff. 62
Riemann surface, regular      186
Riesz, F. and M. (theorem of)      50
Schmidt, E.      21
Schottky's theorem      200
Schottky, G.      200
Schwarz's, lemma      14
Schwarz's, reflection principle      88 ff. 101 211
Schwarz's, triangle functions      173 ff.
Schwarz's, triangle nets, mapping of      185
Schwarz, H.A.      101 130 134
Schwarzian derivative      130
Systems of differential equations      127 ff.
Tetrahedral class      176
Theorem of Dieudonne      19
Theorem of F. and M. Riesz      50
Theorem of Fatou      43
Theorem of Hartogs      114 ff.
Theorem of Jensen      22
Theorem of Julia      27
Theorem of Koebe — Faber      62 ff. 68
Theorem of Landau      197
Theorem of Lebesgue      47 49 50
Theorem of Lindeloef      42 ff.
Theorem of Loewner      34
Theorem of Milloux      107 ff. 109
Theorem of Montel      201 ff. 203
Theorem of Picard, first      199
Theorem of Picard, second      203
Theorem of Pick      14 ff. 23
Theorem of Schottky      200
Topologically equivalent      59
Triangulations      173 ff.
Triangulations, dihedral      175
Triangulations, icosahedral      176
Triangulations, octahedral      176
Triangulations, tetrahedral      176
Unit functions      12
Universal covering surface      71 80
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