Narasimhan R. — Analysis on Real and Complex Manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Narasimhan R. — Analysis on Real and Complex Manifolds

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Название: Analysis on Real and Complex Manifolds

Автор: Narasimhan R.

Аннотация:

Advanced Studies in Pure Mathematics consists of monographs and expository texts. It will cover important recent developments in contemporary mathematics, as well as topics for which a satisfactory systematic modern treatment is lacking. The editors hope that the existence of this series will tempt potential authors to fill some of the many gaps in the literature which are being felt by an increasing number of workers in various mathematical fields. Advanced Studies in Pure Mathematics will include books in English and French, and, possibly, translations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 1973

Количество страниц: 246

Добавлена в каталог: 18.10.2010

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Предметный указатель

$C^{k}$ function      54
$C^{k}$ manifold      52
$C^{k}$ map      54
$C^{k}$ structure      53
$\overline{\partial}$ -acyclic open set      137
adjoint of a differential operator      181
Almost complex manifold      123
Analytic function      3 54
Analytically dependent functions      25
Analyticity Theorem      225 227
Borel's, E. theorem      30
Boundary of a manifold      97
Boundary point      97
Bracket of vector fields      73
Bundle map (morphism)      156
Bundle of forms of type (p,q)      162
Bundle of p-forms      64 162
Completely integrable differential system      113
Complex analytic isomorphism      54
Complex manifold      53
Coordinate neighbourhoods      53
Coordinate systems      53
Coordinate transformations      53
Cotangent bundle      63 162
Cotangent space      56
Covector      56
Critical point      20 66
de Rham cohomology groups      91
Derivation      56
Diffeomorphism      4 54
Differentiable manifold      52
Differential      56
Differential form of degree p      70
Differential form of type (p,q)      78
Differential form, closed      91
Differential form, complex valued      76
Differential form, exact      91
Differential form, holomorphic      93
Differential of a function      14
Differential of a map      60
Differential operator      172
Differential system      112
DIMENSION      52 53
Direct sum of vector bundles      160
distribution      112
Dual of a vector bundle      161
Elliptic linear differential operator      179
Exterior derivative 86 exterior power of a vector bundle      161
Finiteness theorem      231
Formal adjoint      181
Formal transpose      183
Fourier transform of a function in $L^{1}$       165
Fourier transform of a function in $L^{p}$       167
Friedrichs' inequality      207
Frobenius' theorem 1st form      116
Frobenius' theorem 2nd form      117
Frobenius' theorem 3rd form      120
Functional dependence      25
Garding's inequality      202
Germ of functions      55
Grassmann manifolds      69
Grothendieck's lemma      131 132
Hartog's continuation theorem      136
Holomorphic functions      4 54
Holomorphic map      54
Holomorphic vector fields      79
Imbedding      141
Imbedding, closed      141
Imbedding, locally proper      141
Immersion      141
Implicit function theorem      18 76
Integrable almost complex structure      124
Integral of a differential system      112

Integration of differential forms      104
Interior point      97
Invariant vector field      110
Inverse function theorem      18 65
Inverse image (of a differential form)      73
Involutive differential system      113
Jacobi identity      74
k-connected manifold      149
Linear differential operator      172
Linear differential operator with analytic coefficients      183
Local one parameter group      106
Local operator      87
Locally finite family      11
Locally proper map      81
m-flat      28
Malgrange — Lax approximation theorem      236
Manifold      52
Manifold with boundary      96
Newlander — Nirenberg theorem      125 126
Oka — Weil theorem      139
One parameter group      106
Order of a linear differential operator      176
Orientable manifold      94
Orientation      94
Partial differential      15
Partition of unity      11 66
Plancherel theorem      168
Poincare's lemma      128
Positive covector      99
Positive tangent vector      98
Projective space      69
Proper map      81
Pull-back of a differential form      73
Rank of a map 64 rank theorem      18 65 76
Rapidly decreasing function      165
Real analytic function      3 54
Real analytic isomorphism      54
Real analytic manifold      52
Regular map      141
Regularity theorem      217 227
Rellich's lemma      193 228
Runge domain      38
Runge's theorem      239
Sard's theorem      20 66
Section of a vector bundle      163
Sobolev spaces      184 185
Sobolev's lemma      197
Stationary function      56
Stein manifold      239
Stokes' theorem      104
Strongly differentiable in $L^{p}$       189
Strongly elliptic operator      201
Structure forms on an almost complex manifold      123
Submanifold      80
Support of a function      3 54
Support of a section      163
Symbol of a linear differential operator      179
Tangent bundle      63 162
Tangent space      56
Tangent vector      56
Tensor product of vector bundles      161
Thorn's transversality theorem      154
Transition functions      157
Transpose of a differential operator      183
Transversal map      151
Uniformly strongly elliptic      201
Vector bundles      155
Vector fields      69
Weierstrass'approximation theorem      33
Whitney's Approximation Theorem      34 35
Whitney's extension theorem      31
Whitney's imbedding theorem      146
Whitney's immersion theorem      145
Whitney's sum      160

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