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| Nehari Z. — Conformal mapping |
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| Предметный указатель |
"Modern Analysis" 206 316
Absolute convergence 57
Absolute convergence of an infinite product 285
Absolute value 53
Accessory parameters 202
Addition theorem, exponential function 71 280
Addition theorem, logarithm 80 93
Addition theorem, trigonometric functions 74 277 279
Analytic continuation 103—105
Analytic curve 42 186 341
Analytic function, branch of 76
Analytic function, definition of 59
Analytic function, definition of, global 102
Analytic function, element of 104
Approximation 256
Approximation in the mean 245
Area of a conformal map 154 362
Area theorem 210
Argument of a complex number 53
Argument principle 130
Automorphic functions 313
Bergman kernel function 250—260 367—376 389 391
Bessel functions 116
Bessel inequality 245
Bilinear transformation 156
Boundary point 1
Boundary point, inaccessible 178
Boundary value problem 14 19 23 181 357
Bounded functions in multiply-connected domains 378—392
Bounded functions in the unit circle 166—168
Branch of an analytic function 76
Branch point 78 152
Canonical domains 189 333
Canonical mappings, existence of 342
Capacity 183
Cassinian 270
Cauchy integral formula 94
Cauchy — Riemann equations 28 62
Cauchy's inequality 100
Cauchy's theorem 84
Circle of convergence 66 99
Circle with circular slits 336
Circular ring 336 373
Circular slit mapping 335
Closure 1
Closure, cn z 281
Compactness 141
Complement 1
Complete sets of functions 245 370
complex numbers 49
Complex numbers, argument of 53
Complex numbers, conjugate of 51
Complex numbers, modulus of 53
Complex numbers, sequences of 55—56
Complex plane 53
Complex variable 58
Confocal conies 270 274
Confocal conies, domains bounded by arcs of 299—308
Conformal equivalence 174
Conformal map, area of 154 362
Conformal mapping, definition of 149
Conformal type 333
Conjugate of a complex number 51
Conjugate of a harmonic function 28 62
Connected set 2
Connectivity of a domain 3
Continuous deformation 32 90
Continuous function 58
Continuous functional 144
contour 84
Contour integration 90
Convergence of a product 285
Convergence of a sequence 55
Convergence of a series 57
Convergence, absolute 57
Convergence, uniform 66 96
Convex domains 222—224
cos z 72 274
Critical point 133 150 153
Cross ratio 158
Crosscut 2
Curvilinear polygon 198 204
Curvilinear triangle 207
Derivative 59
Diagonal process 142
Differentiable function 59
Dirichlet problem 14 354
Discontinuity 21
Distortion theorems 214
dn z 281
Domain 2 153
domain functions 42
Domain of definition 58
Doubly periodic functions 282 288 298
Doubly-connected domains 3 33 334
Element of an analytic function 104
ellipse 258 270 279 295 300
Elliptic function 280—299
Elliptic function, Jacobian 281
Elliptic function, modulus of 292 319
Elliptic integrals 281
Elliptic modular function 318—332
Entire functions 118 321
Equicontinuity 137
Essential singularity 112 113
Existence of canonical mappings 342
Exponential function 70—74 273—274
Extremal problems 145
Fixed points of a linear transformation 161
Fourier coefficients 244 373
Function element 104
Functional 144
Functional equation, permanence of 106—107
Fundamental theorem of algebra 118 121 135
Gamma function 109
Gauss' theorem 6
Global definition of an analytic function 102
Goursat's lemma 87
Green's formula 8 9 12 240
Green's function 13 38 133 181 187 357
Green's function, symmetry of 14
Green's function, variation of 42
Group of linear transformations 160 313
Hadamard's three-circle theorem 120
Hadamard's variation formula 46
Harmonic conjugate 28
Harmonic function, conjugate of 28 62
Harmonic function, definition of 4
Harmonic function, maximum principle for 9
Harmonic measure 38 357
Holomorphic function 59
Horizontal slit mapping 362
Hyperbola 269 270 307
Hyperbolic functions 79
Hypergeometric series 206 314
imaginary numbers 49
Imaginary part 51
Inaccessible boundary point 178
| Infinite products 284—286
Infinite series 56—58
Inner product 241
Integration 81—84
Interior point 1
Inverse function 74 281 308
Inverse points 162
inversion 184 190 310
Inversion principle 184
Jacobian elliptic functions 281
Jordan curve 2
Joukowsky profile 271
Kernel function 250—260 367—376 389
Laplace equation 4
Laurent series 110—111
Legendre polynomial 97
Lemniscate 270
Limit point 1 56 137
Line integral 6
Linear independence 242
Linear transformation 155—165
Liouville's theorem 117
Local uniform boundedness 138
Log z 74—77 273
Logarithmic residue 128
Many-valued functions 74
Mapping theorem, Riemann 175
Maximum principle 119
Maximum Principle for harmonic functions 9
Meromorphic part 116
Modular surface 320
Modulus of a complex number 53
Modulus of a doubly-connected domain 334
Modulus of an elliptic function 292 319
Monodromy theorem 108
Montel's theorem 141
Morera's theorem 95
Multiply-connected domains 2 7 32 89 333
Natural boundary 108 311
Nearly circular domains 47 263—265
Neighborhood 1
Neumann function 23
Neumann problem 25 31
Norm of a function 241
Normal families 140 217
Odd function 213 328
Open set 1
Order of a branch point 78 153
Order of a pole 112
Order of a zero 113
Orthogonal circle 309
Orthogonal functions 242
Orthogonalization process 242
Orthonormal sets of functions 243 370 389
Outer area 361
parabola 269 279 305—307
Parallel slit mappings 334
Parameters, accessory 202
Parseval's identity 100
Partial fractions 116
Period 35 73
Period parallelogram 290
Period rectangle 283
Permanence of a functional equation 106—107
Picard's theorem 321
Piecewise smooth curve 2
Point at infinity 3 112
Poisson formula 17 97
Poisson kernel 17
Pole 112 128—131
Polygon 189
Polynomial 60
Positive real part, functions with 169—171
Potential 4
Power series 65—70
Power, general 77
Principal part 116
Principal value 75
Principle of permanence 106—107
Radial slit mapping 335
Radius of convergence 66 69
Radius of convexity 224
Radius of starlikeness 354
Rational functions 60 114
Rational functions of second degree 266—273
Real part 51
rectangle 280
Reflection principle 184
Regular function 59
Reproducing property 250 361 368 389
Residue 122
Residue theorem 122
Riemann 173
Riemann mapping theorem 175
Riemann moduli 334 354
Riemann surface 76 78 80 231 266
Ring with circular slits 336
Robin constant 183
Rouche's theorem 131
Schlicht domain 154
Schlicht function 209
Schmidt orthogonalization process 242
Schwarz lemma 165
Schwarz — Christoffel formula 194
Schwarzian derivative 199 226
Schwarzian s-functions 308—318
Sequences of analytic functions 140—143
Sequences of complex numbers 55—56
Simple pole 123
Simply-connected domains 2
sin z 72 274—277
Single-valued functions 59 76
Singular point 5 59 99
Smooth curve 2
sn z 280
Starlike domains 220—222
Subordination 227
Symmetry principle 184
Szegoe kernel function 389
tan z 277—278
Taylor series 69 98
Tchebichef polynomials 258
Three-circle theorem 120
Transcendental entire functions 118
Transfinite diameter 183
triangle 194
Triangle functions 308
Triangle, curvilinear 207
Trigonometric functions 72 274—280
Typically real functions 225
Uniform boundedness 138
Uniform convergence 66 96
Unimodular linear transformations 331
Univalent functions 146 209—226
Variation of the Green's function 46
Vertical slit mapping 362
Whittaker — Watson 206 316
Zeros of an analytic function 113 128—132
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