Hormander L. — The analysis of linear partial differential operators I :: Электронная библиотека попечительского совета мехмата МГУ

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Hormander L. — The analysis of linear partial differential operators I

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Название: The analysis of linear partial differential operators I

Автор: Hormander L.

Аннотация:

"This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation."

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 1990

Количество страниц: 440

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(x\pm i0)^{a}$       72
$<u, \varphi>$       44
$A^{'}(\mathds{R}^{n})$       331
$b_{\Gamma}(f)$       342
$C^{1}$       7 143
$C^{1}$ boundary      59
$C^{k}$       11 143
$C^{k}_{0}$       14
$C^{L}$       281
$C^{M}$       22
$C^{\gamma}$       123 241
$C^{\infty}_{0}$       14
$d_{j}$       160
$f^{(k)}(x; y_{1}, ..., y_{k})$       11
$f_{*}$       148
$H_{(s)}$       240
$H_{K}$ (supporting function)      105
$L^{1}_{loc}$       37 143
$L^{2}_{s}$       240
$N_{e}(F)$       300
$N_{f}$       263
$N_{i}(F)$       301
$P(x, \partial)$       13
$P^{(\alpha)}$       13
$sing supp_{A}$       282
$sing supp_{L}$       282
$WF^{'}_{Y}$       268
$WF_{A}$       283 340
$WF_{L}$       283
$WF_{X}$       268
$x^{a}_{+}$       68 69
$x^{a}_{-}$       71
$y^{\alpha}$       13
$\alpha!$       13
$\alpha$ (multi-index)      12
$\ast$ (convolution)      16 88 101
$\Box$       139
$\check{u}$       71 164
$\chi^{a}_{+}$       73
$\circ$ (composition)      131 133
$\delta_{a}$       56
$\Gamma^{\circ}$ (dual cone)      257
$\hat{u}$       160 164
$\mathscr{D}^{'k}$       34
$\mathscr{D}^{'}$       34 144
$\mathscr{D}^{'}_{F}$       34
$\mathscr{D}^{'}_{\Gamma}$       262
$\mathscr{E}^{'k}$       45
$\mathscr{E}^{'}$       45
$\mathscr{S}$       160
$\mathscr{S}^{'}$       163
$\omega$ (canonical one form)      149
$\partial/\partial z$ , $\partial/\partial\bar{z}$       62
$\partial^{\alpha}$       12
$\partial_{j}$       12
$\sigma$ (sympletic form)      152
$\subset$       43
$\tilde{q}$       189
$\tilde{u}$       108
$\triangle$       80
$\underline{x}^{-k}$       72
$\| \|_{(s)}$       240
$|\alpha|$ (its length)      12
A      326
A'(K)      326
Adjoint operator      272
Advanced fundamental solution      141
Ai (Airy)      213
Airy differential equation      214
Airy function      213
Analytic functional      326
Asgeirsson mean value theorem      183
Atlas      143
b(x)      335 337
beta function      86
Bicharacteristic (strip)      154 302
Bicharacteristic curve      302
Borel theorem      16
Canonical one form      149
Canonical transformation      155
Carrier of analytic functional      326
Cauchy integral formula      63
Cauchy problem      141 349
Cauchy — Kovalevsky theorem      348
ch (convex hull)      105
Chain rule      8
char      271 315
Characteristics      152 271 350
Conormal bundle      149
Convex function      90 91
Convex hull      105
Convolution      16 88 101
Coordinate system, patch      142
Cotangent bundle      148
Critical point      218
Cutoff function      25
Denjoy — Carleman theorem      23
density      145 148
Diagonal      131
Diagonal map      267
Differential form      148 150
Differential operator      13
Differentiate      7
Dirac measure      56
Direct product      126 127
distribution      33
Distribution on manifold      144
Distribution, density      145
Dual cone      257
Dual cone, quadratic forms      206
Edge of the wedge theorem      343 344
Elliptic operator, polynomial      111 169 271
Essential support      322

Exponential solution      185
f'(x)      7
f* (pullback)      134 149 263 345
Feynman fundamental solution      141
Finite part      70
Fourier inversion formula      161 164
Fourier transform      160 164
Fourier — Laplace transform      165
Fundamental solution      80
Gamma function      73 86
Gauss — Green formula      60
Gevrey class      281
H (Heaviside)      56
Hamilton vector field      153
Hamilton — Jacobi theory      157
Hardy — Littlewood — Sobolev inequality      117
Heaviside function      56
Hoelder continuity      123
Holmgren uniqueness theorem      309
Homogeneous distribution      74
Hyperbolic polynomial      320
Hyperfunction      335 337
Hypoelliptic operator      110
Inverse function theorem      9
Kashiwara — no-Holmgren theorem      364
Kernel theorem      128
Kolmogorov equation      210
Lattice point      28
Leibniz' formula      13
Manifold      142 143
Manifold real analytic      282
Measure      38
Microhyperbolic      318
Microlocal analysis      251
Multi-index      12
Multiple layer      136
N(F)      301
Normal bundle      149
Normal of map      263
Normal set      300 301
Order of distribution      34
Orientation      150
Oscillatory integral      238
P(D)      182
Paley — Wiener — Schwartz theorem      181
Parametrix      170
Parseval's formula      163
Partition of unity      28
Phase function      236
Plurisubharmonic function      96
Poisson bracket      156
Poisson summation formula      178
Polydisc      346
Positive distribution      38
Principal part (symbol)      151 271
Principal type      275
Principal value      73
PRODUCT      55 267
Proper cone      10 257
Proper map      104
Pullback of distribution      135 263
Pullback of form      149
Pullback of hyperfunction      345
PV (principal value)      73
Quasi-analytic class      22
Real analytic function      24 281
Regular set      52
Regularization      17
Retarded fundamental solution      141
Runge theorem      112
Schwartz kernel theorem      129
Section of vector bundle      147
Sequential continuity      35
sgn (signature)      85
Signature      85
Simple layer      136
sing supp      42
Singular support      42
Slowly varying metric      28
Sobolev embedding theorem      123
Sobolev spaces      240
Stationary phase      215 218
Stationary points      218
Stieltjes — Vitali theorem      110
Subharmonic function      92
Supp      14 41
Support of analytic functional      331
Support of distribution      41
Support of function      14
Support of hyperfunction      336
Supporting function      105
Supports, theorem of      107
Symbol      237
Symplectic form      152
Symplectic map      155
Tangent bundle      147
Tangent cone of set      364
Tangent vector      146
Taylor's formula      12
Temperate distribution      163
Tensor product      126 127 267
Test function      14
Transition matrices      147
TRANSPOSE      112
Transversal intersection      266
Trivialization of vector bundle      147
Vector bundle      146
Vector field      148
Wave front set      254 265 283 340
Weak solution      2
Weak topology of distributions      38
WF      254
WF'      268
Whitney extension theorem      48

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