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Авторизация |
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Поиск по указателям |
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Bergman S. — The Kernel Function and Conformal Mapping |
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Предметный указатель |
44
46
44
50
57
47
21
44
51
46
, period of 46
79
79
77
45
57
21
1
118
45
47 59
Affine transformations 142
Ahlfors method 150
Analytic continuation 18
Analytic hypersurface 145
Analytic surface 145
Analyticity in a variable 132
Approximation to analytic functions 13
Approximation to analytic functions, to solutions of elliptic differential equations 117
Average quadratic error 3
B-harmonic function 148
Basic space 33
Bessel inequality 3
Bicylinder 132
Boundary of four-dimensional domain 133
Boundary value problem of first and second kinds 112
Bounded functions 86
Canonical domains 61
Canonical mapping functions, in terms of kernel function 71
Cauchy formula 133 147
Cauchy sequence 41
Cauchy — Riemann equations 46 132
Circular domain 134
Class 47
Class 45
Class 57
Class 1
Class 118
Classical domain functions 44
Closed orthogonal system for a simply-connected domain 12
Closed orthogonal system, existence of 10
Closed orthonormal system for 118
Closed system 3 135
Closed system of orthogonal harmonic functions 47
Closed system, construction of 10
Compact family 10 15
Complete space 41
Complex derivatives 35
Countable basis of H 41
Curvature, bounds for 36
Determinantal notation 25
Differential equations, of elliptic type 112
Differential equations, of elliptic type, non-definite coefficient 122
Differential geometry 31
Differential operators 35
Dirichlet integral 44 115
Dirichlet integral as metric 48
Dirichlet problem 52 112
Dirichlet problem, solved using kernel function 52
Distinguished boundary curve 147 150
Distinguished boundary surface 133 144
Distortion of length 140
Distortion of length, bounds for 142
Distortion theorems 67 71 96 144
Distortion theorems for two complex variables 138
domain functions 44
Domain functions, monoticity of 95
Domain, admitting a group of stability 142
Domain, admitting a group of stability for which polynomials are closed 13
Domain, admitting a group of stability, canonical 61
Domain, admitting a group of stability, of comparison 37 140
Doubly-harmonic functions 148
Doubly-harmonic measures 148
Doubly-orthogonal functions 14
Eigenf unctions 126
Eigenvalues 122
Elasticity equation 127
Elasticity equation, solution of boundary value problems for 130
Elliptic differential equations 40 112
Elliptic functions 10
Entire functions 150
Equation of elasticity 127
Existence of slit mappings 111
Expansion theorems 7 113 117 130 136
Extended class 149
Extremal curves 31
Extremal property of canonical domains 67
First boundary value problem 52
First fundamental form 31
Four-dimensional domains 132
Four-dimensional domains, visualization of 133
Fourier coefficients 2 119
Function of first kind 46 47
Function of second kind 47
Function of third kind 46 47
Functions of extended class 150
Functions of two complex variables 132
Functions of two variables 135
Fundamental solution S(Z, Z) 112
Gaussian 32
Gaussian of invariant metric 35
Gaussian of the metric 38
Gaussian, radius of 32
Gaussian, total 32
Geodesies 31
Gram — Schmidt orthogonalization process 3
Green’s formula 44 45 46
Green’s function 44 58 112 116 128 129 148
Green’s function, construction of 118
Green’s function, eigenfunctions 121
Green’s function, relation to Neumann’s function 50
Green’s function, representation 50 120
Green’s function, representation by kernel function 54
Green’s function, variation of 100
Group of stability 142
Hadamard variational method 90
Harmonic functions 40
Harmonic functions, closed systems of 44
Harmonic measure 45 144 150
Harmonic measure, conjugate harmonic function 46
| Harmonic measure, representation in terms of kernel function 53
Hermitian form 18 27 28 138
Hermitian form, Jacobi reduction of 28
Hilbert space, convergence in 41
Hilbert space, convergence in, definitions 41
Hilbert space, convergence in, of functions 41
Hyperbolic measure, generalization of 144
Hypersphere 133 137 141
Identities connecting domain functions 54
Indicatrix 39
Integral operator of first kind 171
Integrals of first kind 47
Invariant metric, curvature of 35
Invariants of a domain 140
Jacobi reduction 28
Kernel function 41 58 77 106 115 116 120 126 127 129
Kernel function for circle 79
Kernel function for non-bounded, non-schiicht domains 37
Kernel function for simply-connected domains 79
Kernel function in two variables 136
Kernel function of 47
Kernel function of an orthogonal system 9
Kernel function, boundary behavior of 38
Kernel function, boundary relation of 111
Kernel function, canonical mapping functions in 71
Kernel function, extremal property 87 136
Kernel function, harmonic 49
Kernel function, identities 57
Kernel function, independent of closed system 21 136
Kernel function, inequality in terms of 23
Kernel function, invariance of 137
Kernel function, minimum property of 42
Kernel function, monotonicity of 42
Kernel function, relative invariant 33
Kernel function, reproducing property of 22 42 83
Kernel function, uniqueness of 23
Kernel function, variation of 90
Kernel of Cauchy formula 148
Length, an absolute invariant 33
Length, an absolute invariant, of a curve 31
Linear independence 1
Linear space 41
Mapping function, for simply-connected domain 24
Mapping function, for simply-connected domain, existence of 70
Mapping theorems 61
Matrix notation 24
Meromorphic functions 150
Meromorphic functions of several complex variables 148
Method of orthogonal functions 135
Metric 113 122 138
Metric and invariant metric 32
Metric of Pick — Poincare 35
Metric, boundary behavior of 37
Metric, Gaussian curvature of 38
Metric, monotonicity of 34
Minimizing function 21
Minimum area 24
Minimum problem 24 30
Minimum problem and partial differentiation 113
Modulus of doubly-connected domain 102
Monotonic properties of minimum 140
Multiply-connected domains 61
Neumann problem 53 112
Neumann problem, solved with help of kernel function 53
Neumann’s function 44 112 116
Neumann’s function, construction of 118
Neumann’s function, relation to Green’s function 50
Neumann’s function, representation of 50 120
Nevanlinna’s theorems 150
Non-Euclidean length element 141
Norm, in Hilbert space 41
Normal family 17
Normal form 112
Normalization 2
Normed space 41
Orthogonal functions 2
Orthogonalization process 3
Orthonormal functions 2
Orthonormal systems 125
Orthonormal systems for elliptic differential equations 118
Orthonormal systems for equation of elasticity 128
Orthonormalization conditions 135
Parsevai identity 119
Parseval formula 3
Poincaire theorem 138
Polygonal domains 4
Positive definite Hermitian quadratic form 42
Positive definite Hermitian scalar product 41
Positive definite quadratic form 31
Principle, of hyperbolic measure 34
Principle, of hyperbolic measure, of minimum integral 39 144
Projection 121
Pseudo-conformal equivalence 150
Pseudo-conformal invariants 138
Pseudo-conformal transformation 132 138
Pseudo-conformal transformation of one circular domain 137
Pseudo-conformal transformation, invariant of 140
Pseudo-conformal transformation, non-existence of 137
Reinhardt circular domains 135
Representative domains 61
Riemann mapping theorem 34 138
Riemannian manifold 31 33
Riesz — Rischer theorem 5
Robin’s constant 96
Robin’s problem 131
Runge theorem 13
Scalar product 1
Schiffer method 98
Schottky theory 60
Schwarz — Christoffel constants 75
Schwarz’s inequality integral 1 42
Schwarz’s lemma 42
Schwarz’s lemma, generalization 87
Second boundary value problem 53
Simply-connected domains 34
Simply-connected domains for two complex variables 138
Slit mappings 111
Smooth curves 44
Stieltjes integrals 99
Svmmetrv of G and N 44
Symmetry relation for periods 46
Triangle inequality in Hilbert space 41
Variation, of analytic kernel 94
Variation, of analytic kernel, of Green’s function 93 100
Variation, of analytic kernel, of harmonic measures 94
Variation, of analytic kernel, of kernel function 92
Variation, of analytic kernel, of period 95
Variational method, of Hadamard 90
Variational method, of Schiffer 98
Weierstrassian -function 10
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