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Bochner S., Martin W.T. — Several Complex Variables
Bochner S., Martin W.T. — Several Complex Variables

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Название: Several Complex Variables

Авторы: Bochner S., Martin W.T.

Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1948

Количество страниц: 216

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_p$-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 $\log r_1$, ..., $\log r_k$      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 $I_k$      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, $l_p$      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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