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| Bochner S., Martin W.T. — Several Complex Variables |
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| Предметный указатель |
 -norm 116
Abelian function 198
Abelian group 156
Additive measure 20
Adjoint group 156
Adjoint operator 159
Affine transformation 144
Algebraic function 30 198
Algebraic functions on product domains 202
Allowable coordinates 54
Allowable mapping 54
Analytic continuation 34 137
Analytic continuation for analytic in each variable separately 139
Analytic continuation for bounded functions 139
Analytic convexity 72
Analytic function in an analytic coordinate space 55
Analytic function of analytic functions 33
Analytic functions 30
Analytic homeomorphism 45
Analytic manifold at a point 205
Analytically oblique position 144
Analyticity in each variable 32
Analyticity in each variable, Hartogs’ theorem on 32 140
Approximations 109
Arcwise connectedness 196
Automorphism 50
Averaging process 161
Banach space 117
Basis 204
Basis of a tube 90
Basis of radiated domain 78
Behnke, H. 23
Bergman, S. 109
Bieberbach 45
Borel radii 148
Borel transform 149
Bounded groups of transformations 17
Bounded, weakly 12
Canonical form 18
Caratheodory, C 14 164
Cartan, H. 13 48
Cauchy — Riemann equations 36
Channel 79
Characteristic manifold 109 194
Characteristic roots 17
Circular domain 78
Circular domains as representative domains 120
Circular group 10
Circular type, domains of 78
Class few 111
Closed linear subspace 118
Closed, weakly 12
Common zeros 206
Compact group 15
Compact, weakly 12
complete 121
Completion of tubes 96
Completion, analytic 64
Completion, geometric 66;
Completion, z-completion 67
Concentric and co-axial rectangles 97
Conical domain 77
Conjugate complex variables 36
Constant coefficients 161
Continuation, analytic 34 137
Continuity of an analytic function 31
Continuity of group product 20
Continuity theorem 69
Continuous convergence 48
Convergence to the identity 16
Convergent, weakly 12
Convex cone 131
Convex domains 70
Convex function of  , ...,  125
Convex hull 90
Convex shells 70
Convex tube 90
Convexity; analytic, modified 72
Coordinate space; real analytic, complex analytic 54
Crescent-shaped wedges 97
Decomposition 193
Degenerate 182
Degree of an element 190
Derivatives of an analytic function 31
Differentiability properties of approximations 111
Differential form 122
Dilations of a circular domain 146
Discriminant 195
disks 78
Distinguished polynomials 190 192
Domain of absolute convergence 81
Domain of circular type 78
Domain of continuous convergence 78
Domain of multi-circular type 81
Domain of regularity 85
Domain, circular 78
Domain, equivalent 120
Domain, Hartogs 78
Domain, multi-circular 81
Domain, radiated 75
Domain, Reinhardt 81
Domain, representative 120
Domain, smallest convex 131
Domain, star 88
Dominated convergence 104
Elliptical polycylinder 92
Enlarged concept of Lebesgue integrals 104
Environment, real 33
Equivalence in  192
Equivalent domains 120
Exceptional set 171
Exponential growth 126
Extension of rings, separable, simultaneous integral, successive integral, algebraic 209—211
Family, majorized 40 51
Fatou 45
Finite-dimensional vector space 117
Fixed point 50
Formal power series 3
Formal power series, order of a term of 3
Formal power series, ring of 3
Formal power series, vanish 3
Fourier integrals, multiple 128
Frontier, property 84
Fubini’s Theorem 105
Functional relation 174
Functions of mixed variables 35
Functions of real variables 33
Functions, implicit 39
Generalized solutions 158
Group invariant measure 22
Group of transformations 9
Group, abelian 156
Group, adjoint 156
Group, bounded 17
Group, circular 10
Group, compact 15
Group, product, continuity of 20
hadamard 152
Hadamard’s three spheres theorem 59
Half-plane function 147
Half-planes 147
Hardy’s theorem 125
Harmonic function 103 162
Harnack’s theorem 135
Hartogs 103
Hartogs’ domain 78
Hartogs’ domains, largest and maximal 143
Hartogs’ function 143
Hartogs’ main theorem 137
Hilbert spaces 121
| Homeomorphism, analytic 45
Homorphism 10
Hull, convex 90
Hypersphere, analytic completion of the exterior of 71
Ideal 204
Implicit functions 39
Inequality of Jensen — Hartogs 103
Inner product 123
Inner transformations, determinant of 9
Inner transformations, inner mappings 6
Integrability 20
Integrable square 130
Integrity, domain of 191
Invariance of minimal functions 119
Inverse 10
Inverse, left, right 10
Invertible 13
Irreducible 193
Irreducible manifold 206
Isomorphism 10
Iterated transformation 13
Jacobians 38 173
Jacobians, identical vanishing of 174
Jacobians, non-vanishing of 174
Jensen 103
Jensen’s Inequality 135
Kernel 109 122
Laplace equation 163
Largest Hartogs domain, radii of 143
Laurent series 90
Levi, E. E. 41
Levi’s condition 72
Lie group, complex 154
Limit of strict solutions 164
Limit transformation 182
Limit, weak 12
Linear differential operator 159
Linear part of a transformation 10
Lipschitz condition 171
Local analytic varieties 204
Local boundedness 139
Locally compact family 89
Locally connected at a boundary point 87
Lower semi-continuous 76
Majorized family 40 51
Manifold characteristic 194
Mapping, allowable 54
Mapping, topological 45
Matrix of operators 165
Matrix, unitary 58 155
Maximal domains 75
Maximal from below 77
Maximal from below and above 78
Maximal Hartogs domain, radii of 143
Maximum 75
Maximum on the boundary 107
Menchoof — Looman 166
Meromorphic function 152
Meromorphy, radius of 151
Minimal element 119
Minimal functions 119
Modified convexity 72
Monotone convergence 135
Multi-circular type, domains of 81
Multi-periodic function 90
Multi-torus 156
Multiple Fourier integrals 128
Non-degenerate transformation 23
Non-singular transformation 10
Norm, 116
Norms of polynomials 24
Null-divisor 4
Nullifiers 166 168
Octant 132
Operator 159
Orbit 78
Order 3
Orthogonal systems 121
Osgood, W. F. 139
Partial differential equations, generalized solutions of 158
Partial ordering 75
Peschl, E. 23
Phragmen — Lindelof 125
Picard 45
Plancherel 128
Plane, supporting 86
Poincare, H. 109
Poisson kernel 103
Poisson kernel, generalized 136
Poisson’s integral 163
Polycylinder circular 30
Polycylinder circular, generalized 31
Polynomials, norms of 24
Power-scries, formal 3
Preparation theorem, Weierstrass, proof for formal power series 183—188
Preparation theorem, Weierstrass, proof from analytic consideration 188—190
Primary ideal 207
Prime ideal 206
Proper ideal 205
Quotient 183 189
Quotient field 209
Quotient of two analytic functions 152
Radiated, point-set, domain 75
Radius of meromorphy 151
Rate of growth of kernel 123
Rational functions on product domains 199
Reciprocal relations 150
Rectangles, concentric and co-axial 97
Rectifiably connected 113
Reducible 193
Regular element 191
Regular ideal 208
Regularity, domain of 85
Reinhardt analytic completion 82
Reinhardt domain 81
Relative completion 89
Removable singularity 168 169
Representative domains of Bergman 120
Residue class 269
Retrosection, complete 66
Riemannian distance 122
Ring 3
Ruckert, W. 264
Schwarz’s lemma 59
Semi-group 6
Series, formal power 3
Severi, F. 69
Similar transformation 17
Similarity 12
Smallest convex domain 131
Spherical surfaces, mappings of 55
Star domain 88
Strict solution 160
Subharmonic function 145
subspace 118
Supporting plane 86
Supremum 109
Surface integrals 124
Symbolic derivative 37
Symmetric function 189 199
Systems of (differential) equations 169
Testing function 160
Topological mapping 45
Topology, weak 11
Transformation, inner 6
Transformation, iterated 13
Transformation, limit 182
Transformation, linear part of 10
Transformation, non-degenerate 23
Transformation, non-singular 10
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