Pier J.-P. — Mathematical Analysis during the 20th Century :: Электронная библиотека попечительского совета мехмата МГУ

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Pier J.-P. — Mathematical Analysis during the 20th Century

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Название: Mathematical Analysis during the 20th Century

Автор: Pier J.-P.

Аннотация:

Pier, president of the Luxembourg Mathematical Society, traces the evolution of mathematical analysis and explains the development of main trends and problems in the field in the 20th century. Chapters cover areas such as general topology, classical integration and measure theory, functional analysis, harmonic analysis and Lie groups, and topological and differential geometry. There is also material on topics related to analysis, such as probability theory and algebraic geometry. Each chapter features material on development during the period 1900-1950, and then describes representative achievements during the second half of the century. Quotations from outstanding mathematicians are included.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 438

Добавлена в каталог: 07.04.2008

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Предметный указатель

$C^\infty$ -manifold      289
$C^\infty$ -vector field      291
$\mu$ -continuity      60
$\mu$ -distance      60
$\mu$ -harmonic      326
$\sigma$ -additive      63
$\sigma$ -compact      178
*-algebra      115
Abel      158
Abel’s continuity theorem      158
Absolute continuity      65
Absolute mean value      135
Absolute value      161
Absolute value of an element in a C*-algebra      101
Absolutely continuous function      50
Absolutely convex      120
Absorbant set      107
Abstract analysis      146
Abstract Hardy space      219
Abstract harmonic analysis      139
Accumulation point      31 32 41
Adams      345
Adele      172
Adhererent      32
Adjoint mapping      180
Adjoint operator      92
Adjoint representation      190
ADO      189
Affine scheme      279
Ahern      68
Ahlfors      208
Akkouchi      169
AKO      243
Alaoglu      91
Aldous      112
Aleksandrov      218
Alexander, J.      257 260—264 266 271 274 291
Alexander, S.      300
Alexandrov      33 34 40 42 264 265 289
Alexandrov compactification      42
Algebraic analysis      252
Algebraic curve      337
Algebraic group      196
Algebraic integration theory      66
Algebraic number      336
Algebraic polyhedron      225
Algebraic topology      267
Almost connected group      191
Almost everywhere      49
Almost period      140
Almost periodic      140
Almost simple group      193
Alternant      181
Amann      278
Ambrose      99 157
Amenable banach algebra      123
Amenable group      172
Analysis situs      27
Analytic geometry      223
Analytic group      185
Analytic manifold      225 297
Analytic manifold structure      224
Analytic set      217
Analytic space      226
Andler      195
Anosov      237
Antisymmetric tensor      285
Approximately finite-dimensional      117 124 346
Approximation property      117
ARC      256
Archimedes      47
Arcwise connected      257
Aristotle      199
Arnold      247 249
arrow      271
Artin, E.      20 267 338 339
Artin, M.      45 345
Arzela      208
Ascoli      208
Asphericity      111
Asplund      113
Astala      216
Atiyah      v 251 256 306 310 311 312 346 347 348
Atiyah — Singer index theorem      311
Atlas      289
Aubin      128
Auslander      195
Automoiphic function      218
Automoiphism      37
Azencott      194 326
Bachelier      318
Baer      39
Bailey      218
Baire      4 6 31 36 44 113 204
Bakali      169
Baker      181 182
Balanced subset      107
Balayage      60
Banach      61 78 86 87 88 89 90 99 110 111 138
Banach algebra      99
Banach module      116
Banach ring      347
Banach space      90
Banach space geometry      111
Banach — Mazur distance      111
Bargmann      149
Barnard      74
Barrel      107
Barreled space      107
Barycenter      108
Barycentric subdivision      258
Basic filter of neighborhoods      91
Basis of neighborhoods      32
Bass      347
Baum      348
Baum — Connes conjecture      348
Beals      244 252
Beauzamy      112
Behnke      212 213 226
Belfi      116
Berard      301
Berger      127
Berglund      174
Bernoulli measure      329
Bernoulli shift      329
Bernoulli, D.      129
Bernoulli, J.      315
Bernstein      253
Bernstein — Sato polynomial      253
Bers      243
Bertrand      317
Bessaga      112
bessel      82
Betti number      258 263 265
Beurling      159
Bicharacteristic curve      244
Bicommutant      95
Bicommutation theorem      95
Bicompact      33
Bieberbach      205 206 218 236
Bieberbach conjecture      218
Bienaymd      155
Bifurcation      247
Bilinear form      84
bing      37 187
Birkhoff, Garrett      19 78 185 189 231 288
Birkhoff, George      8 9 287
Bishop      108 127
Bismut      15
Blaschke      296

Bochnak      349
Bochner      14 55 140 156 169
Bochner’s theorem      152 156
Bohnenblust      89
Bohr      140 141 143 211
Bohr mean value theorem      140
Bokobza      251
Boks      52
Bolt      251 287 304 312
Boltzmann      328
Bolzano      31
Bolzano — Weierstrass property      31
Bombieri      349
Bonnet      312
Borel field      322
Borel set      47
Borel subgroup      172
Borel — Lebesgue property      31
Borel, A.      14 190 193 194 196 197 198 218 277 343
Borel, E.      25 29 31 32 33 42 47 48 62 184 316 317
Born      6
Bosch      172
Boson      149
Bossut      3
Bouligand      128
Boundary      36 292
Boundary of a chain      262 264
Boundary of a cohomology      40 41
Boundary of a locally compact group      193
Boundary of a simplex      265
Bounded mean oscillation      221
Bounded measure      65
Bounded variation      50
BOUNDING      264
Bourbaki      9 10 13 14 27 28 31 36 44 52 55 63 64 65 66 67 91 95 107 128 189 196 197 332
Bourgain      15 113 122 220 246 326 327
Bracket      189
Brackx      126
Braconnier      155
Braid      267
Braid group      267
Bratelli      117
Brelot      68 209
Bretagnolle      110
Brezis      249
Brjuno      227
Brouwer      127 231 259 260 261 275 278
Brouwer fixed point theorem      259
Browder, A.      114
Browder, F.      79 231 249 278
Brower      127
Brown      318
Brownian motion      324
Bunce      123
Bundle      279
Burke      109
C*-algebra      115
Cairns      297
Calderon      164 170 174 176 177 216 243 244 251
Calderon subset      170
Campbell      181
Campbell — Hausdorff formula      185
Cantor, G.      27 32 39 62 74
Cantor, M.      62
Capacity      60
Caratheodory      55 56 57 58 64 66 135 155 210
Carleman      135 235 243
Carleman’s asymptotic formula      301
Carleson      108 165 171 222
Carleson set      171
Carleson’s theorem      165
Carriere      303
Cartan subalgebra      192
Cartan subgroup      172 192
Cartan, E.      10 137 173 180 181 182 183 184 185 186 188 189 190 193 194 234 237 274 280 283 284 285 289 298 300 341
Cartan, H.      vi 13 14 41 42 60 63 68 140 141 144 152 187 188 213 214 224 225 226 279 311 343 346
Cartier      10 71 344
Casimir      188
Catalan      4
Catastrophe theory      247
Category      45 271
Cauchy      12 30 31 33 253
Cauchy formula      226
Cauchy — Kowalewska theorem      234
Cavalieri      3 63 104
Cayley      142
Cech      40 42 43 268 291
cell      258 261 262 266 269
Central limit theorem      315
Cernavskii      308
Chain      40 258 261 263 265
Chaos      249
Character of a Banach algebra      99
Character of an abelian group      150
Charbonnel      195
Chart      289
Chem      283 284 297 299 312
Chern character      311
Chern class      297
Chevalley      42 162 163 171 172 185 187 188 191 193 194 196 297 333 343
Chevalley group      193
Chittenden      30
Choquel capacity      68
Choquel representation theorem      108
Choquet      68 107 323
Christoffel      283
Clarke      306
Clarkson      91
Classical analysis      19
Classical groups      185
Clausius      328
Clifford algebra      126
Closed      35
Closed ball      33
Closed drain      263 264
Closed set      34
Closed subset      32
Closure      36
Closure finite      272
Coarser topology      34
Cobordism      303
Coboundary      291
Cochain      116 259 291
Cocycle      116 259
Cohen's factorization theorem      115
Cohen, P.J.      115 166
Cohen, R.      306
Coherent sheaf      226
Cohomology      291
Cohomology group      116 259
Coifman      220 221
Cole      249
Collet      250
Combinatorial proof      308
Combinatorial topology      267
Commutant      95
Compact      30 32
Compact factor      192
Compact Lie algebra      193
Compact operator      109 110
Compact-open topology      117
Compactification      43
complete      133
Complete normed vector space      86
Complete orthonormal system      80
Complete reducibility      188
Complete regular space      42
Complete space      33
Complete system of neighborhoods      39
Completed projective tensor product      119

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