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Hormander L. — The Analysis of Linear Partial Differential Operators IV
Hormander L. — The Analysis of Linear Partial Differential Operators IV

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Название: The Analysis of Linear Partial Differential Operators IV

Автор: Hormander L.

Аннотация:

The first two volumes of this monograph can be regarded as an expansion and updating of my book "Linear partial differential operators" published in the Grundlehren series in 1963. However, volumes III and IV are almost entirely new. In fact they are mainly devoted to the theory of linear differential operators as it has developed after 1963. Thus the main topics are pseudo-differential and Fourier integral operators with the underlying symplectic geometry. The contents will be discussed in greater detail in the introduction.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 352

Добавлена в каталог: 13.12.2009

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Предметный указатель
Admissible perturbation      279
Asymptotic completeness      277
Asymptotic sum      66
Besov space      472
Bicharacteristic      310
Bicharacteristic, broken      426
Bicharacteristic, foliation      74
Bicharacteristic, generalized      434
Bicharacteristic, one dimensional      97
Bicharacteristic, relation      69
Bicharacteristic, two dimensional      112
Blowup      128
Bott operator      209
Calderon projector      236
Calderon uniqueness theorem      220
Canonical relation      290
Canonical transformation      271
Cauchy problem      385
Characteristic      87 251 27
Clean composition      291
Clean intersection      491
Clean phase function      292
Coerciveness      234
Commutation relations      271
Compressed broken bicharacteristic      426
Compressed cotangent bundle      130
Compressed generalized bicharacteristic      435
Condition $(\bar{\Psi})$      96
Condition $(\Psi)$      96
Condition (P)      110
Cone supp      448
Conic manifold      278
Conormal distribution      100
Covering condition      234
Darboux homogeneous      279
Darboux theorem      273
Diffractive set      432
Dirichlet principle      28
Dirichlet problem      24
Distorted Fourier transform      277
Douglis — Nirenberg operator      228
Eiconal equation      104
Elliptic boundary problem      233
Elliptic complex      222
Elliptic operator      87 27
Elliptic set      424
Energy integral method      47 386 418 443 118 286
Excess      292 491
Exponential map      37
Fefferman — Phong inequality      171
fold      492
Foliation      487
Fourier $L^{2}$ continuity      25 48
Fourier composition      21 47
Fourier integral operator      17 43
Fredholm complex      189
Fredholm operator      181
Friedrichs' lemma      9
Frobenius theorem      485
Fundamental matrix      321
g continuity      142
Generalized bicharacteristic      434
Generalized geodesic      272
Generating function      26
Geodesic coordinates      32 500
Glancing hypersurfaces      311
Glancing set      431
Gliding ray      432
Gliding set      432
Gliding vector field      434
Hadamard construction      30
Hamilton field      71 272
Hamilton foliation      286
Hamilton map      321
Hilbert — Schmidt operator      185
Hyperbolic set      424
Hypoelliptic operator      348
Hypoelliptic set      461
Hypoelliptic symbol      350
INDEX      181 351
Involution      493
Involutive submanifold      285
Involutive subspace      283
Isotropic submanifold      285
Isotropic subspace      283
Isotropic vector      417
Jacobi identity      272
Kolmogorov equation      353
Lacunary condition      114
Lagrangian distribution      4
Lagrangian submanifold      285
Lagrangian subspace      283
Lagrangian, Grassmannian      328
Lagrangian, ideal      36
Lagrangian, positive ideal      40
Leaf of foliation      487
Lefschetz formula      223
Lie derivative      22
Limiting absorption principle      295
Lopatinski — Schapiro condition      234
Lorentz signature      417
Manifold with boundary      482
Manifold with corner      129
Maslov bundle      334
Melin's inequality      364
Microhypoelliptic      348
Microlocal property      80
Microsubelliptic      165
Modified distorted Fourier transform      314 327 329
Modified wave operator      309
Nirenberg — Treves estimate      134
Non-degenerate fixed point      225
Non-degenerate of positive type      37
Non-degenerate phase function      292
Parametrix      34 87 223 238
Poisson bracket      271 272
Polyhomogeneous symbol      67
Positive canonical ideal      43
Positive Lagrangian ideal      40
Positive plane      325
Principal symbol      86 104 228 243 13
Principal type      65 163
Principally normal      238
Proper composition      18
Properly supported      86
Pseudo-convex      67
Pseudo-differential adjoint      69 159
Pseudo-differential change of variables      81
Pseudo-differential continuity      74 75 162 164 169
Pseudo-differential multiplication      71 155
Pseudo-differential operator      68 85
Pseudo-differential parametrix      72 87 88
Pseudo-local property      80
Quasi-concave      145
Radial vector field      277
Real principal type      65
Refined principal symbol      93
Reflected exponential map      38
Reflection bundle      494
Semi-bicharacteristic      96
Semi-concave      145
Sharp Garding inequality      76 170 178
Short range      279
Slowly varying metric      142
Solvability      92 94
Spacelike vector      417
Spectral function      44
Stretched product      129
Strictly hyperbolic operator      394
Strongly pseudo-convex      239
Subelliptic      165 166
Subprincipal symbol      83 161
Symbol      65 142
Symplectic basis      270
Symplectic density      274
Symplectic form      269
Symplectic isomorphism      270
Symplectic manifold      271
Symplectic subspace      283
Symplectic vector space      269
Symplectomorphism      271
Temperature metric      153
Temperature weight      153
Timelike vector      417
Totally characteristic differential operator      113
Totally pseudo-differential operator      131
Trace class operator      187
Transmission condition      105
Transversal composition      19 44
Transversal ellipticity      361
Transversal intersection      490
Transversal order      483
Tricomi operator      405
Twisted canonical relation      294
Weakly continuous form      147
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