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Friedlander F.G. — The Wave Equation on a Curved Space-Time
Friedlander F.G. — The Wave Equation on a Curved Space-Time

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Название: The Wave Equation on a Curved Space-Time

Автор: Friedlander F.G.

Аннотация:

This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1975

Количество страниц: 282

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{\infty}$ structure      3
adjoint of a differential operator      49 65
Adjoint of a tensor differential operator      203
Advanced potential      117
Affine connection      10
Affine parameter      12
Analytic continuation      53
Analytic space-time      141
Bicharacteristic      79
Bijective      265
Bitensor      204
Boundary of a manifold      5
Boundary of a set      263
Cauchy problem      50
Cauchy problem for a scalar wave equation      181 249
Cauchy problem for a tensor wave equation      211
Causal curve      147
Causal domain      146
Caustic      88
Characteristic      51 77
Characteristic initial value problem      76 193
Chart      3
Closed set      263
Closure      263
Codimension      5
Compact set      264
Continuous function (map)      265
Convolution      43
Coordinate neighbourhood      3
Coordinate system      3
Coordinate transformation      3
Cotangent bundle      8
Cotangent space      7
Covector      5
Cross-section      6
Curvature      11
Curve      5
d'Alembertian      12
de Rham operator      27
Delta function      see "Dirac delta function"
Dependence domain      129
Descent, method of      251
Diffeomorphism      4
Differential operator      49
Dirac delta function      32
Dirac delta function, on a manifold      65
Discontinuity of order k      92
Distribution of finite order      34
Distribution on $R^{n}$      32
Distribution on a manifold      60 63
Distribution topology      see "Weak topology"
Distribution with compact support      38
Divergence      11
Divergence theorem      26
Dual of a topological vector space      269
emission      138
Exponential map      14
Exterior, differential      21
Exterior, form      20
Exterior, product      20
Finite part      54
Flux of a vector field      26
Focal point      88
Fourier — Laplace transform      256
Function      265
Fundamental solution      52 65
Fundamental solution of a scalar wave equation      154 240
Fundamental solution of a tensor wave equation      207
Future-compact      169
Future-directed      73
Geodesic      12
Geodesic distance      17
Geodesically convex domain      15
Gradient      7
Hadamard series      146
Hausdorff space      263
Heaviside function      121
Homeomorphism      266
Huygens' principle      221
Hyper surf ace      5
Imbedding      4
Improperly posed      123
Induced orientation      26
Infective      265
Initial value problem      50
Initial value problem for characteristics and null fields      81
Inner product      9
Integral of an exterior form      23
Invariant volume element      25
Kernel distribution      246
Kirchhoff's formula      124
Laplacian      12
Leray form      68
Lienard — Wiechert potential      219
Line source      212
Linear form      268
Local coordinates      3
Locally finite      4
Locally integrable      23
Lorentzian metric      9
m-surface      5
Manifold      2
Manifold-with-boundary      5
Metric      9
Minkowskian chart      72
Multi-index      29
Neighbourhood      262
Normal coordinates      16
Normal neighbourhood      15
Null, cone      129
Null, field      76
Null, geodesic      80
Null, hyper surface      75
Null, semi-cone      129
Null, vector      73
Open set      262
Ordinary wave equation      72 229
Orientable      23
Orientation      22
Orientation-preserving chart      23
Orthogonal vectors      74
Paracompact      4
Parametrix      144
Partition of unity      4
Past-compact      169
Past-directed      73
Progressive wave      101 104
Propagator      see "Transport bitensor"
Proper map      48
Properly posed      123
Pseudo-Riemannian metric      9
Regularization      47
Resolving kernel      151
Restriction      265
Retarded potential      117
Riemann function      242
Riemannian metric      9
Scalar product      7
Semi-norm      267
Semi-norm estimate      32
Sequentially continuous      266
Signature      9
Space-like field      76
Space-like hyper surface      75
Space-like vector      73
Space-time      72
Spatial boundary      175
Sub-manifold      4
Support of a distribution      33
Support of a function      4
Support of an exterior form      20
Surjective      265
Tail term      158
Tangent bundle      6
Tangent space      6
Tangent vector      6
Tensor      8
Tensor distribution      63
Tensor product of distributions      40
Tensor product of tensors      8
Tensor wave equation      109 203
Test function      30
Time orientation      73
Time-like field      76
Time-like hypersurface      75
Time-like vector      73
Topological space      262
Topological space, vector space      266
topology      262
Topology, induced      263
Topology, product      263
Transport bitensor      205
Transport equation, scalar      96 104
Transport equation, tensor      109
Trivial transformation      159
Vector      see "Tangent vector"
Vector field      6
Volume element      see "Invariant volume element"
Wave equation      72
Wave front      177
Weak solution      49
Weak topology      34
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