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Kato G., Struppa D.C. Ч Fundamentals of algebraic microlocal analysis
Kato G., Struppa D.C. Ч Fundamentals of algebraic microlocal analysis

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Ќазвание: Fundamentals of algebraic microlocal analysis

јвторы: Kato G., Struppa D.C.

јннотаци€:

Provides a thorough introduction to the algebraic theoryof systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1999

 оличество страниц: 296

ƒобавлена в каталог: 06.12.2009

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\mathcal{C}^\infty$ function      26 97 107
$\mathcal{D}$-module      vii 2 61 81 151 157Ч162 166Ч168 170Ч176 179Ч181 183 209 211 225 226 235 267
Abelian category      151 152 154 163 164 196 198
Adjoint      69 184 185 243 244 247
Algebraic analysis      v viii 2 81 156 157 160 178Ч180
Algebraic geometry      v vii 81 82 151 156 157 160 180 261
Algebraic microlocal analysis      vЧvii 91
Associated sheaf      65 106
Berenstein      viii
Bicharacteristic curve      253
Bicharacteristic manifold      269Ч271
Bicharacteristic strip      253Ч255 257 258 273
Bjoerk      145
Bochner      47 79
Bochner tube theorem      47
Bogolyubov      85 87
Bogolyubov's theorem      86 87
Boundary value      v vi 6 7 11 13 14 18 29 36 37 45 46 48 52 53 55 57 59Ч62 66 75 81 85Ч89 94 107Ч113 117Ч119 133 134 139 140 145 254
Boundary value representation      39 62
Boutet de Monvel      264
Canonical filtration      175 191
Carleman      72 79Ч81
Carleman's fourier theory      79
Cartan      180 232
Cartan's theorem      4 52 88
Category      153 164 183 185 196 198 203 204 224 231 236 237
Cauchy      4 6 16 18Ч20 65 76 78 86 124 139 211 214 249 251 252 272 273
Cauchy Ч Hadamard theorem      16
Cauchy Ч Kowalewsky theorem      82 209 211Ч213 215 245 249
Cauchy Ч Riemann operator      97
Cauchy Ч Riemann system      270 271 273
Cauchy's existence and uniqueness theorem      224
Cauchy's existence theorem      24 25
Cauchy's theorem      7 9 11 62 223
Cech cohomology      52
Characteristic variety      97 151 174 200 206 214 217 223 224 231 237 239Ч241 253 262Ч265 270 271
Coboundary      52Ч55 58 188
Cochain      53 54 58 151
Cocycle      22 58 81 83 88
Coherent      178 197 198 203 204 211 212 216 217 230
Cohomology      vi vii 3 21 55 60 61 64 66 71 81 83 88 155 162 165Ч167 180 183 192 194 200 201 204 206 215 216 219Ч222 226 228Ч230 233 236
Cohomology functor      152 154 202
Cohomology sheaf      193 197 203 231
Commutator      258
Complex neighborhood      2Ч4 6Ч10 14 18 19 22 24 25 28 29 32 39 40 43 44 51 52 65 66 86Ч89 108 125
Complexification      230
Conormal bundle      106
Contact manifold      256 257 262
Contact transformation      255 257Ч259 262 271 273
Convex      43 48 59 70 71 87
Convex cone      48 54 56 57 59 65 86Ч89 117 148
Convex hull      47 86 88
Convex set      56 124
Convolution      84 138 140
Convolution operator      84 98 138
Cotangent bundle      v vii 93 95 107 144 176 256 257
Darboux theorem      257
de Rham complex      166 183 188 193Ч195
de Rham functor      161 183 193 194 198 224 237
De Rham module      161 235
De Rham system      223 262 263 269 273
Delta function      11 12 28 31 40 59 73 74 93 94 116
Derived category      vii 151Ч154 159 162Ч164 180 199 203 224 235Ч238
Derived functor      160Ч163 193 196 202Ч204 234
Derived sheaf      49 51 59
Differential operator      v vii 8 12 24Ч26 30 31 39 40 61 69 92 96 98 100Ч102 108 122 130 131 133 157 162 169 170 175 176 181 183 185 200 209 210 212 239 241 244 245 249 253 266 267
Dirac      11Ч13 15 31 40 59 60 73 74 110 135 201
Direct image      115 120 121 209 218Ч221
Direct limit      154 202
Domain of holomorphy      43 81 125
Double complex      151 154 155 232 233
Dual cone      56 57
Dual space      56 58
Edge of the wedge theorem      62 63 73 75 85 88 89 111 112 127
Egorov      258
Ehrenpreis      vi viii 41 70 79 94 147 240
Ehrenpreis fundamental principle      272
Ehrenpreis Ч Palamodov fundamental principle      41 79 239
Eilenberg      232
Elliptic operator      30 100 101 248
Ellipticity      30 31 33 248
Entire function      23 44 63 72 84 94 98
Epstein      87
Essential support      141
Euler's fundamental principle      30 240
Exact sequence      5 66 68 70 88 115 116 118 156 157 159 173Ч176 191 192 200Ч203 213 215 217 221 222 231
Excision theorem      52
Exponential type      94 98
Ext functor      270
Ext module      71
Faithful      178 203 204 206 237
Fantappie'      9 19 72 75Ч78 81Ч83
Fantappie' Ч Koethe Ч Martineau Ч Sato duality theorem      21
Fantappie' Ч Sato indicatrix      77
Filtration      155 169Ч173 181 203Ч205
Finite dimensionality theorem      230
Finite order differential operator      40 241
Finite resolution      72
Flabby resolution      24 60 70 228
Flabby sheaf      vi 5 21Ч23 27 36 65Ч67 111 113Ч115 119 133 269 270
Flat      95 178 197 202Ч204 216
FOURIER      73
Fourier transform      38 41 72 79 80 84 93 94 96Ч98 106 116 135 138 140 142 143 146 148
Free resolution      69 159 167 188Ч190 193Ч195 204 207 212 216 220 221 223 230
Frobenius existence theorem      224
functor      5 61 106 120 152 153 162Ч165 175 183 185 192 193 196Ч198 200 201 203 204 206 213 224 231 232 237 238
Fundamental solution      98 135 241 246 249
Fundamental theorem      261
Germ      3 16 17 23 26 37 38 40 50 61 70 74 81 116 123 125 127 157 159 161 165 169 176 183 184 200Ч202 209
Good filtration      151 170Ч173 175 190Ч192 204Ч207 217 223 237
Grauert      65
Grauert theorem      88
Grothendieck      72 78 81 82 180
Hahn Ч Banach theorem      41 148
Hamiltonian operator      269
Hamiltonian vector field      257
Hartogs' removable singularities theorem      81
Hartogs' theorem      43
Hartshorne      81 157 180
Harvey      50 70
Heaviside      73 74 84
Heaviside function      12 13 34 73 94 242
Heaviside hyperfunction      12 29
hilbert      74
Hilbert nullstellensatz      175 176
Hilbert sygyzy theorem      72
Hilbert's basis theorem      69 156
Hoermander      v 1 70 92 107 134 141 142 258 272
Holmgren's theorem      249 252
Holomorphic function      vi 3Ч8 13Ч17 20 22 23 26 28 31 34 36 37 39 40 42Ч46 48Ч50 52 53 55 58Ч61 65 70 72 75Ч77 80Ч83 85 87Ч89 107 108 112Ч114 117 123 125 127 131 132 134 140 145 159 161 165 169 170 174 176 177 183 236 241 258 263
Holonomic module      162 181 194 199 200 203 209 222Ч226 231 234 235 237
Holonomic system      162 262
Homogeneous polynomial      100 131 170 176
Homotopy      152
Hyperbolic operator      255 273
Hyperderived functor      164 165 196 220Ч222
Induced filtration      171 204
Inductive limit      7 23 28 32 37 40 41 51 61 70 119
Infinite order differential operator      14 16 17 40 73 83 122Ч124 130 176 265 267 269
Infinitesimal wedge      47 48 52 59 65 112 117 128
Initial value problem      82
Inverse image      4 116 218
Kaneko      2 21 50 65 142
Kashiwara      v vii viii 2 117 119 180 181 191 209 229 237 238 273
Kashiwara's constructibility theorem      223 225 231 236 237
Kawai      v vii viii 2 38 72 80 180 230 231 237 273
Kimura      v 2
Koethe      14 37 72 75 77 78
Koethe's duality theorem      21 41 42 75
Komatsu      31 50 61 70 180
Koszul complex      189 190 192
Kowalewsky      78 214
Kree      264
Lagrangian      226 262
Lagrangian analytic set      226
Lagrangian bracket      257
Lagrangian manifolds      262
Laurent expansion      15 16
Laurent series      18 200
Left exact contravariant functor      162 230
Left exact functor      161 163Ч165 198
Leray spectral sequence      120
Leray's theorem      52 57
Lewy      271 273
Lewy Ч Mizohata      271 273
Linear finite order differential operator      24 31
Liouville's theorem      20
Local operator      17 18 29Ч31 39 84 129 130
Local system      224
localization      152 164 176
Locally closed      49 50 224 226
Locally finite      22 27 64 65 114 146 226
Lutzen      78 79
Malgrange      66 70 86
Malgrange Ч Zerner's theorem      86
Malgrange's theorem      43 68
Martineau      50 72 83 86 88 89 127
Maslov      258 273
Maximally overdetermined system      262
Mayer Ч Vietoris theorem      63
Mebkhout      183 198 199
Mebkhout's theorem      183 200
Mellin transform      84
Microanalytic      108 109 112 113 115 116
Microdifferential operator      124 125 130Ч133 176Ч178 239 240 259Ч261 263 264 266 268 271 273
Microlocal analysis      v 1 79 83 84 134 141 180 273
Microlocal operator      92 96 120 122 125 127 129Ч133 240Ч247
Microlocalization      1 8 26 36 93 95 96 107 176 241 272
Microsupport      104
Mittag Ч Leffler theorem      3 22 25 32 43 50 115
Mizohata      272 273
Morera theorem      6
N-th derived sheaf      49 51
Noetherian ring      181 203
Non-characteristic      212 214Ч216 227
Non-local operator      84
Order (of differential operator)      31
Painleve      5 85 86
Painleve's theorem      6 85
Palamodov      viii 70
Paley Ч Wiener theorem      93 98 142 144
Paramterix      96 98 100Ч102 239
Pincherle      17 83 84
Plane wave decomposition      116 246
Poincare      76
Poincare duality      199
poisson      73
Poisson bracket      257 271
Presheaf      36 49 66 106 114 116 177
Principal symbol      97 99 131 170 172 178 223
Projective resolution      159 161 162 167 197 216 232 235
Pseudo-differential operator      96 98 102Ч105 107 122 124 127
Purely n-codimensional      49Ч51
Quantized contact transformation      240 241 259Ч262 267 269
Quotient sheaf      36 65 66 116
Real analytic category      110
Real analytic function      6 7 11 13 26Ч29 37 38 42 61 69 93 110 115 125 142 230 242 245 247 248
Relative cochain      54 58
Relative cohomology      42 48 52 57 59 61 63 70 71 81Ч83 88 120
Relative covering      52Ч54 57
Residue      116 136
Resolution      70 161 183 189 220
Riemann Ч Hilbert correspondence theorem      181 236
Riemann Ч Hilbert Ч Kashiwara Correspondence theorem      237
Right derived functor      164
Ring of differential operators      178
Sato      v vii viii 1 2 8 24 27 49 50 72Ч75 79Ч83 85 91 107 179Ч181 239 240 262 265 272
Sato's fundamental exact sequence      248
Sato's fundamental principle      25 131 240 253 254
Sato's fundamental sequence      114
Sato's fundamental theorem      151 176 178 239 241 245 248 250 261 264 272
Sato's structure theorem      vii
Sato's theorem      241 244
Schapira      viii 50
Schwartz      v 1 7 18 30 36 41 67 69 74 78 81 93 139 240
Schwartz's kernel theorem      101
Serre      180
Serre duality      199 200
Sheaf      vi vii 1 3 17 21Ч31 36 37 42 44 49Ч51 60 61 63Ч71 81 83 84 89 91Ч93 106 107 111 113Ч116 119 120 122Ч126 128Ч130 132 133 140 157 159Ч163 165 169 170 176Ч178 180 183 184 187 193 197 198 200 203 209 210 216 218 221 223 225Ч228 230 240 246 253 263 267 269 270
Sheaf of microdistributions      106
Singular spectrum      92 108 109 112 119 126Ч128 134 141 145 246 247
Singular support      28 29 36 92 93 105 108 111 212
Skew category theory      180
Slowly decreasing      72
Spaeth theorem      268
Spectral decomposition mapping      115
Spectral sequence      52 81 151 154 155 162 163 165 166 180 195Ч197 199 200 221 233Ч235
Spectral sequence of a composite functor      163 164 198
Spheric cotangent bundle      93 111
Stalk      50 51 169 200 203 206 217 225 228
Standard denning function      19 42
Stein covering      57
Stein domain      50
Stein neighborhood      51 88
Struppa      72
Subsheaf      27 36 63 92 116 132 177 187
Support of a hyperfunction      111
Symbol of an operator      93
symbols      103
Symplectic geometry      256
Symplectic manifold      256 257
Symplectic structure      257
Tube domain      140
Tubular neighborhood      46
Universal property      152
Verdier      180
Virtual bicharacteristic manifold      271
Wave operator      249 253
wedge      46 47 58 59 85
Weierstrass      84 212
Weierstrass' division theorem      263 268
Weil      75 81 180
Weyl's lemma      247
Zerner      86
Zorn's lemma      67
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